Can someone please tell and show me the steps on how to do this I need help

One bagel costs 155 cents.

An algebraic expression is the combination of numbers and variables in expressing and solving a particular mathematical question.

Let x = cost of one bagel

y = cost of one toast

z = cost of one muffin

If two pieces of toast and a bagel costs $3.15, then 2y + x = 3.15.

2y + x = 3.15   ⇒   x = 3.15 - 2y     (equation 1)

If a bagel and a muffin costs $3.30, then x + z = 3.30.

x + z = 3.30     (equation 2)

Substitute equation 1 to equation 2.

x + z = 3.30     (equation 2)

3.15 - 2y + z = 3.30   ⇒   z = 0.15 + 2y      (equation 3)

If a piece of toast, two bagels, and three muffins costs $9.15, then

y + 2x + 3z = 9.15     (equation 4)

Substitute equations 1 and 3 to equation 4.

y + 2x + 3z = 9.15     (equation 4)

y + 2(3.15 - 2y) + 3(0.15 + 2y) = 9.15

y + 6.30 - 4y + 0.45 + 6y = 9.15

3y = 2.4

y = 0.8

Substitute the value of y to equation 1.

x = 3.15 - 2y     (equation 1)

x = 3.15 - 2(0.8)

x = 1.55

Hence, the cost of one bagel is $1.55 or 155 cents.

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The equation of each line in slope intercept form y = 2x + 3,x = 4

The equation of a line in slope-intercept form (y = mx + b), the slope (m) and the y-intercept (b). The slope-intercept form is a convenient way to express a linear equation.

Equation of a line with slope m and y-intercept b:

y = mx + b

Equation of a vertical line:

For a vertical line with x = c, where c is a constant, the slope is undefined (since the line is vertical) and the equation becomes:

x = c

An example for each case:

Example with given slope and y-intercept:

Slope (m) = 2

y-intercept (b) = 3

Equation: y = 2x + 3

Example with a vertical line:

For a vertical line passing through x = 4:

Equation: x = 4

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Answer:

y=mx+b

Step-by-step explanation:

the null hypothesis (H0) represents the statement that there is no significant difference or effect, while the alternative hypothesis (Ha) states the opposite.

to determine if there is enough evidence to support the claim that the mean annual return is indeed greater than 3.6 percent or not.In hypothesis testing, the null hypothesis (H0) represents the statement that there is no significant difference or effect, while the alternative hypothesis (Ha) states the opposite.

In this case, the null hypothesis is that the mean annual return for the employee's IRA is at most 3.6 percent. It suggests that the true mean return is equal to or less than 3.6 percent. Mathematically, it can be represented as H0: μ ≤ 3.6, where μ represents the population mean.

The alternative hypothesis, Ha, contradicts the null hypothesis and asserts that the mean annual return is greater than 3.6 percent. It suggests that the true mean return is higher than 3.6 percent. It can be represented as Ha: μ > 3.6.

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Answer:

156 students

Step-by-step explanation:

To find how many students are in choir this year, multiply 120 by 1.3

120(1.3)

= 156

So, this year, 156 students are taking choir

Answer:

156 students

Step-by-step explanation:

120*30%=36

120+36=156

x rounded to 1 decimal place is approximately 3.4 cm.

To work out the value of x, we can use the trigonometric function cosine (cos).

The cosine of an angle is defined as the ratio of the length of the adjacent side to the length of the hypotenuse in a right triangle.

In this case, the length of the adjacent side is

x, and the length of the hypotenuse is 6 cm.

The given angle θ is 55°.

Using the cosine function, we have:

\(cos(\theta ) =\frac{adjacent }{hypotenuse}\)

\(cos(55^{\circ}) =\frac{x}{6}\)

To solve for x, we can rearrange the equation:

\(x = 6 \times cos(55^{\circ})\)

Now we can calculate x using the given values:

\(x \approx 6 \times cos(55^{\circ})\)

\(x \approx 6 \times 0.5736\)

\(x \approx 3.4416\)

Therefore, x rounded to 1 decimal place is approximately 3.4 cm.

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The minimum number of terms required for the sum sn to have an error less than 0.0399, assuming K = 1 and b-a = 1.

To determine the minimum number of terms n required for the sum sn to have an error less than 0.0399, we need to use the formula for the error term of a finite series:

|En| ≤ ((M * (b-a)^n)/(n!))

where En is the error term, M is the maximum value of the (n+1)th derivative of the function, a and b are the limits of integration, and n is the number of terms in the series.

Since we do not have a specific function or limits of integration, we cannot determine the exact value of M. However, we can use an upper bound for M, which is the maximum value of the (n+1)th derivative of the function over the entire interval [a,b]. Let's assume that M = K, where K is some constant.

Then we have:

|En| ≤ ((K * (b-a)^n)/(n!))

We want the error to be less than 0.0399, so we can set up the following inequality:

((K * (b-a)^n)/(n!)) < 0.0399

To solve for n, we need to use a numerical method such as trial and error, or a graphing calculator. We can also use a table of values for n! and (b-a)^n to simplify the inequality.

For example, if we assume that K = 1 (which is a reasonable assumption for many functions), and let b-a = 1 (i.e. we are integrating over the interval [0,1]), we can create a table of values for n! and (b-a)^n:

n | n! | (b-a)^n
--|----|---------
1 | 1  | 1
2 | 2  | 1
3 | 6  | 1
4 | 24 | 1
5 | 120| 1
6 | 720| 1

Using these values, we can rewrite the inequality as:

(K/n!) < (0.0399/(b-a)^n)

Plugging in our values, we get:

1/n! < 0.0399

Solving for n using trial and error or a graphing calculator, we find that n = 4 is the minimum number of terms required for the sum sn to have an error less than 0.0399, assuming K = 1 and b-a = 1. However, keep in mind that this value may change depending on the specific function and limits of integration.

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Answer:

Step-by-step explanation:

By using the concept of division, it can be calculated that

The statement given in the fourth option

Two pizzas are shared equally among zero people do not have a solution

What is division?

Division is the process by which value of single unit can be calculated from the value of multiple unit.

The number to be divided is known as dividend, the number by which the dividend is divided is the divisor, the result obtained is the quotient and the remaining part is the remainder.

There is a well known formula for division

Divisor x Quotient + Remainder = Dividend.

This is a word problem on division.

For the first option

Number of pizzas = 6

Number of person = 3

Number of pizzas each person get = 6 \(\div\) 3 = 2

This problem has a solution.

For the second option

Number of pizzas = 3

Number of person = 2

Number of pizzas each person get = 3 \(\div\) 2 = 1.5

This problem has a solution.

For the third option

Number of pizzas = 0

Number of person = 3

Number of pizzas each person get = 0 \(\div\) 3 = 0

This problem has a solution.

For the fourth option

Number of pizzas = 2

Number of person = 0

Number of pizzas each person get = 2 \(\div\) 0

Now anything divided by zero is not possible

This problem do not have a solution.

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The direction cosines and direction angles will be - \(\frac{x}{r},\frac{y}{r},\frac{z}{r}\) and

cos⁻¹(\(\frac{x}{r}\)), cos⁻¹(\(\frac{y}{r}\)),cos⁻¹(\(\frac{z}{r}\)) respectively.

The direction cosines of a specified vector, m = xi + yj + zk, are the cosines of the angles it makes well with x, y, and z axes.

The direction cosines of m are cos a, cos b, and cos c  in the x, y, and z axes, respectively, if a forms the angles a,b and c (which are the direction angles) with the x, y, and z axes, respectively.

Let us consider equation as =  \(xi + yj +zk\)

vector of the equation will be - (x,y,z)

r = length of vector = \(\sqrt{x^{2} +y^{2} +z^{2} }\)

The direction cosines will be -

\(\frac{x}{r},\frac{y}{r},\frac{z}{r}\)

angles will be - cos⁻¹(\(\frac{x}{r}\)), cos⁻¹(\(\frac{y}{r}\)),cos⁻¹(\(\frac{z}{r}\))

Let us consider an example,

If we have vector as (1,2,3)

= i + 2j + 3k

= r = \(\sqrt{1^{2} +2^{2} +3^{2} }\)

= \(\sqrt{14}\)

Direction cosines will be -

\(\frac{1}{\sqrt{14} } , \frac{2}{\sqrt{14} }, \frac{3}{\sqrt{14} }\)

Angles will be -

cos⁻¹(\(\frac{1}{\sqrt{14} }\)), cos⁻¹(\(\frac{2}{\sqrt{14} }\)),cos⁻¹(\(\frac{3}{\sqrt{14} }\))

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Answer:

The ratio of girls to total students is 12:30, which can be simplified to 2:5.

Step-by-step explanation:

You can express the ratio in different ways by using the same numbers, for example, you could say that for every 2 girls, there are 5 total students, or that for every 5 total students, 2 of them are girls.

The quotient of the division is 2x^2 + 4x + 1, the remainder is -4, and P(-1) = -4.

The remainder theorem states that if you divide a polynomial P(x) by (x - a), the remainder is equal to P(a). In this case, we need to find P(-1) for the polynomial P(x) = 2x^3 + 2x^2 - 3x - 7.

Let's perform the division of P(x) by (x - (-1)), which simplifies to (x + 1):

2x^2 + 4x + 1

= x + 1 | 2x^3 + 2x^2 - 3x - 7 - (2x^3 + 2x^2)

= - 3x - 7 + (3x + 3)

= - 4

The quotient is 2x^2 + 4x + 1, and the remainder is -4.

Now, let's find P(-1) by substituting x = -1 into the original polynomial P(x):

P(-1) = 2(-1)^3 + 2(-1)^2 - 3(-1) - 7

= -2 + 2 + 3 - 7

= -4

Therefore, the value obtained is -4.

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The first pair of electrons go axially. The second pair go equatorially. Hence, the correct answer is axial; equatorial

For the trigonal bipyramidal electron domain geometry, the first pair of electrons will go to the equatorial position because it has less electron-electron repulsion than the axial position. The second pair of electrons will go to the axial position because the axial position has more space and less repulsion from the equatorial pairs.

Six atoms make up the molecular geometry, with one in the middle and the other five forming a triangle pyramid. The atoms on either side of the center have different bond angles. The compounds phosphorus pentachloride and phosphorus pentafluoride are two examples of trigonally bipyramidal molecules.

To reduce electron-electron repulsion, the initial pair of electrons would prefer to occupy one of the axial locations. The axial locations are further apart from each other compared to the equatorial positions, which are closer together. Hence, axial positioning of the initial pair of electrons would provide a shape that is more stable. According to the VSEPR theory, the remaining electron domains (i.e., lone pairs and/or bonded pairs) would be dispersed among the other places once the initial pair of electrons occupy an axial position.

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The common ratio is 3 which is greater than 1 so the sum of the provided series is not possible.

It is defined as the systematic way of representing the data that follows a certain rule of arithmetic.

We have an infinite geometric series:

1/81 + 1/27 + 1/9 + ....

The common ratio r = (1/27)/(1/81) = 81/27 = 3

Here the value of r = 3

Which is r > 1

As we know to find the sum of the infinite series the common ratio must lie between -1 to 1 or:

-1 < r < 1

As we have r > 1 so the sum is not possible.

Thus, the common ratio is 3 which is greater than 1 so the sum of the provided series is not possible.

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Answer:

its "This infinite geometric series diverges."

Step-by-step explanation:

i took the quiz

The change in total revenue brought about by a 16 unit increase in Q is -1.5.

(a) (i) To differentiate y = 4x⁴ − 2x² + 28 with respect to x, we apply the power rule of differentiation. We have:
dy/dx = 16x³ - 4x

(ii) To differentiate f(x) = 1/x² + √x³ with respect to x, we can apply the chain rule of differentiation. We have:
f(x) = x⁻² + x³/²
df/dx = -2x⁻³ + 3/2x^(3/2)

(iii)(a) The slope of the function y = 3x² − 4x + 5 at x = 4 and x = 6 can be found by differentiating the function with respect to x. We have:
y = 3x² − 4x + 5
dy/dx = 6x − 4
At x = 4,
dy/dx = 6(4) − 4 = 20
At x = 6,
dy/dx = 6(6) − 4 = 32

(b) The second-order derivative of the function y = 3x² − 4x + 5 at x = 4 can be found by differentiating the function twice with respect to x. We have:
y = 3x² − 4x + 5
dy/dx = 6x − 4
d²y/dx² = 6
The second-order derivative at x = 4 is 6. The slope of the function at x = 4 is positive, so we would expect the second-order derivative to be positive.

(b) (i) The demand equation is given by: P = aQ⁻² + b
The marginal revenue function is the derivative of the total revenue function with respect to Q. The total revenue function is:
R = PQ
Differentiating both sides with respect to Q gives:
dR/dQ = P + Q(dP/dQ)
Since P = aQ⁻² + b,
dP/dQ = -2aQ⁻³
Substituting into the equation for dR/dQ, we have:
dR/dQ = aQ⁻² + b + Q(-2aQ⁻³)
dR/dQ = aQ⁻² + b - 2aQ⁻²
dR/dQ = (b - aQ⁻²)
Therefore, the marginal revenue function is:
MR = b - aQ⁻²

(ii) To calculate the marginal revenue when Q = 3b, we substitute Q = 3b into the marginal revenue function:
MR = b - a(3b)⁻²
MR = b - ab²/9
To find the change in total revenue brought about by a 16 unit increase in Q, we can use the formula:
ΔR = MR × ΔQ
where ΔQ = 16
ΔR = (b - ab²/9) × 16
To show that ΔR = -1.5, we need to use the given relationship a > 0 and b > 0. Since a > 0, we know that ab²/9 < b. Therefore, we can write:
ΔR = (b - ab²/9) × 16 > (b - b) × 16 = 0
Since the marginal revenue is negative (when b > 0), we know that the change in total revenue must be negative as well. Therefore, we can write:
ΔR = -|ΔR| = -16(b - ab²/9)
Since ΔQ = 16b, we have:
ΔR = -16(b - a(ΔQ/3)²)
ΔR = -16(b - a(16b/3)²)
ΔR = -16(b - 256ab²/9)
ΔR = -16/9(3b - 128ab²/3)
ΔR = -16/9(3b - 16(8a/3)b²)
ΔR = -16/9(3b - 16(8a/3)b²) = -16/9(3b - 16b²/9) = -16/9(27b²/9 - 16b/9) = -16/9(3b/9 - 16/9)
ΔR = -16/9(-13/9) = -1.5

Therefore, the change in total revenue brought about by a 16 unit increase in Q is -1.5.

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Answer:

false

hypotension will always be the longest

Answer:

false

Step-by-step explanation:

If the statements offered as premises are true, and the conclusion follows naturally from those premises, then a deductive argument is considered to be valid

What is Function?

A function is a relationship between a number of inputs and outputs. A function is, to put it simply, an association between inputs where each input is linked to exactly one output. For each function, a domain, codomain, or range exists.

The values that are specified inside a function when the function is called are referred to as a "argument." However, the parameters are the variables that are defined when the function is declared.

true statement : all dogs have hair

true statement : clifford is a dog.

true statement : clifford has hair

Conclusion is true

If the statements offered as premises are true, and the conclusion follows naturally from those premises, then a deductive argument is considered to be valid. Deductive Argument based on logic ie reasoning out to get a valid inference.

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The degree of the given polynomial is 2 and the leading coefficient is 5. The given expression is 5a^(2)+2a+6. It is a polynomial expression.

The degree of a polynomial is the highest power of the variable in the polynomial. In this case, the highest power of the variable a is 2, so the degree of the polynomial is 2.

The leading coefficient of a polynomial is the coefficient of the term with the highest power of the variable. In this case, the term with the highest power of the variable a is 5a^(2), so the leading coefficient is 5.

Therefore, the degree of the given polynomial is 2 and the leading coefficient is 5.

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Answer:

x = -9 also called undefined slope.

Step-by-step explanation:

And if the line is like this ____________ it is zero slope and the equation is the number that is passes through the y- intercept.

Hope this helps.

x = -9

Answer:

x=-9

I hope this is good enough:

Answer:

BC= 29

Step-by-step explanation:

If the total, AC, is 54 and AB is 25 subtract those two to find the last part, BC.

15% of the time, the probability that student who chose to walk has been late.

From the stated data-

37.5% of the 40% of students who walk to school have been late.

Thus,  37.5% of 40%

= 0.375 x 0.40

= 0.1500

= 15%

Thus, 15% of the time, the student who chose to walk has been late atleast once .

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The complete question is-

At a large high school 40 percent of the students walk to school, 32 percent of the students have been late to school at least once, and 37.5 percent of the students who walk to school have been late to school at least once. One student from the school will be selected at random. What is the probability that the student selected will be one who both walks to school and has been late to school at least once?

Answer:

9

Step-by-step explanation:

Was this a joke or something

The statement that is true regarding the recipe for a mixed berry pie is option C: The recipe calls for 1 ounce of blackberries for every 1 ounce of raspberries.

The recipe for a mixed berry pie requires 5 ounces of blackberries for every 9 ounces of raspberries. To determine the ratio between blackberries and raspberries, we can simplify the ratio by dividing both numbers by their greatest common divisor, which in this case is 1.

By dividing 5 ounces of blackberries and 9 ounces of raspberries by 1, we get a simplified ratio of 5:9. This means that for every 5 ounces of blackberries, we need 9 ounces of raspberries.

To express this ratio as a statement, we can say that the recipe calls for 1 ounce of blackberries for every 1 ounce of raspberries. This matches option C: The recipe calls for 1 ounce of blackberries for every 1 ounce of raspberries.

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Answer:

the answer is I'll either go with c or d

In the given 3D space truss, there are two external forces applied: a 2 kN force at a 45° angle and a 4 kN force. To determine the forces acting in the truss members, a structural analysis is required.

To analyze the forces in the truss members, we can start by resolving the applied forces into their x, y, and z components. The 2 kN force at a 45° angle can be resolved into x, y, and z components using trigonometry. Assuming the positive x-axis is to the right, the positive y-axis is upward, and the positive z-axis is outward from the viewer's perspective, the resolved components of the 2 kN force are approximately 1.41 kN in the x-direction, 1.41 kN in the y-direction, and 0 kN in the z-direction.

Next, we can analyze the equilibrium of the truss by considering the force and moment balance at each joint. By applying the principles of statics, we can calculate the internal forces in the truss members. The 4 kN force and the resolved components of the 2 kN force will generate internal forces in the truss members.

To determine whether each member is in tension or compression, we compare the calculated internal forces to the members' orientation. If the internal force is positive, the member is in tension, and if it is negative, the member is in compression. By examining the calculated internal forces in each member, we can identify whether they are in tension or compression.

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The ordered pair that is the solution of the given system of inequalities is (2, -2)

A relationship between two expressions or values that are not equal to each other is called inequality.

Given is a system of inequalities, y < -x and 2x+y > 2, we need to determine solution set of the given system of inequalities,

The inequalities are,

y < -x....(i)

2x+y > 2

y < 2-2x...(ii)

To find the ordered pair, put y = -x in equation Eq(ii) and replace < by =

-x = 2 - 2x

x = 2

y = -2

Therefore, the ordered pair, is (2, -2) {look at the graph attached}

Hence, the ordered pair that is the solution of the given system of inequalities is (2, -2)

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A linear relationship between the cost of fire damage (y) and the distance from the house to the nearest fire station (x) is being analyzed using the equation y = mx + c.

We have,

A sample of 15 recent fires and the variables recorded for each fire:

x = distance from the fire to the nearest fire station (in miles) and

y = cost of damage (in dollars).

The distances range from 0.7 miles to 6.1 miles.

To determine the linear relationship between the variables x and y, you can perform a linear regression analysis to find the equation of the best-fit line that represents this relationship.

This equation will help you predict the cost of fire damage based on the distance to the nearest fire station.

If you have the data points for the distances and costs of damage, you can use statistical software or tools to perform the regression analysis and find the equation of the line.

The equation will be in the form of:

y = mx + b

where:

y is the cost of damage

x is the distance to the nearest fire station

m is the slope of the line (reflecting the rate of change of cost with respect to distance)

b is the y-intercept (the cost when the distance is 0)

This linear equation will provide insights into how the cost of fire damage changes as the distance to the nearest fire station changes.

Thus,

A linear relationship between the cost of fire damage (y) and the distance from the house to the nearest fire station (x) is being analyzed using the equation y = mx + c.

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a. The critical value for testing if the correlation is significant at α=0.05 with a sample size of 15 is 0.524.

b. With a correlation coefficient of 0.961, the correlation between cost and distance is significant at α=0.05, as the computed correlation coefficient is greater than the critical value of 0.524.

c. The regression equation for predicting cost of damage from the distance between the fire and the nearest fire station is y = 4919x + 10278, where y represents the cost of damage and x represents the distance between the fire and the nearest fire station.

d. To predict the cost of damage for a house that is 0.5 miles from the nearest fire station, substitute x=0.5 into the regression equation to obtain y = 13877 dollars.

Here, we have to test if the correlation is significant, we need to calculate the critical value using the formula: critical value = t(α/2, n-2), where t is the t-distribution value and α is the level of significance.

With α=0.05 and n=15, the critical value is 0.524. As the computed correlation coefficient of 0.961 is greater than the critical value, we can conclude that the correlation between cost and distance is significant.

To find the regression equation, we use the formula: y = bx + a, where b is the slope and a is the y-intercept.

Given that the slope is 4919 and the y-intercept is 10278, the regression equation is y = 4919x + 10278.

This equation can be used to predict the cost of damage for any distance between the fire and the nearest fire station.

To predict the cost of damage for a house that is 0.5 miles from the nearest fire station, we substitute x=0.5 into the regression equation to obtain y = 4919(0.5) + 10278 = 13877 dollars.

This means that the predicted cost of damage for a house that is 0.5 miles from the nearest fire station is $13,877.

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complete question:

An insurance company determines that a linear relationship exists between the cost of fire damage in major residential fires and the distance from the house to the nearest fire station. A sample of 15 recent fires in a large suburb of a major city was selected. For each fire, the following variables were recorded:

x= the distance between the fire and the nearest fire station (in miles)

y= cost of damage (in dollars)

The distances between the fire and the nearest fire station ranged between 0.7 miles and 6.1 miles.

a. The correlation between cost and distance is 0.961. What is the critical value for testing if the correlation is significant at α=.05?

b. The correlation between cost and distance is 0.961. Test if the correlation is significant at α=.05.

c. What is the regression equation for predicting cost of damage from the distance between the fire and the nearest fire station when the slope is 4919, and the y-intercept is 10278 ?

d. Predict the cost of damage for a house that is 0.5 miles from the nearest fire station.

Answer:

false

Step-by-step explanation:

outliers can be neglected especially when working out the mean

Therefore, The statement that "outliers are extreme values above or below the mean that require special consideration" is True.

Explanation:
Outliers are extreme values that lie significantly above or below the mean. They have special considerations because they can affect the interpretation of the mean and standard deviation. For instance, if an outlier is included in the dataset, the mean will be different from when it is excluded, making the mean unreliable. Therefore, outliers should be examined carefully to determine if they represent a genuine value or an error.

Therefore, The statement that "outliers are extreme values above or below the mean that require special consideration" is True.

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To determine if a matrix is a linear combination of other matrices, we need to check if it can be written as a weighted sum of those matrices where the weights are scalar values (numbers).

If a matrix can be expressed in this way, it is said to be a linear combination of the other matrices.

For example if we have matrices: A, B & C and we can write matrix D as follows:

Then D is a linear combination of matrices A, B and C. This concept is important in linear algebra as it allows us to express one matrix in terms of others. Making it easier to manipulate & analyze the matrices. A matrix is a linear combination of other matrices if it can be expressed as a weighted sum of those matrices where the weights are scalar values.

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\(8\div \cfrac{2}{3}\implies \cfrac{8}{1}\div \cfrac{2}{3}\implies \cfrac{8}{1}\cdot \cfrac{3}{2}\implies \cfrac{8}{2}\cdot \cfrac{3}{1}\implies 4\cdot 3\implies 12\)

Answer: The second answer.

Step-by-step explanation: