Let T = R^2 --> R^2 be a linear transformation that sends e1 to x1 and e2 to x2If T maps (8,7) to the vector y..
y = ?
Enter your answer as an ordered pair, such as (1,2)

Answer:

area of figure (a) = 152cm²

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same method will be used to solve ( b) and (c)

Answer:

X= Y/200 - 3/2

Step-by-step explanation:

Answer:

6

Step by step explanation:

8 × ¾ = ²⁴⁄₄ = 6

Answer:

6

Step-by-step explanation:

You can solve this equation in multiple ways:

1) Change \(\frac{3}{4}\) into a decimal

2) Change \(8\) into a fraction, and multiply that way.

The solution to the given system of equations is x = 3 and y = 1.

To solve the system of equations by elimination, we'll eliminate one variable by multiplying one or both of the equations by appropriate constants so that the coefficients of one variable will cancel each other out when we add or subtract the equations.

Let's solve the given system:

1. Multiply the first equation by 3 and the second equation by 2 to make the coefficients of 'x' equal:

Equation 1: 2x + 4y = 10

Equation 2: 3x + 5y = 14

Multiply Equation 1 by 3: 3(2x + 4y) = 3(10) becomes 6x + 12y = 30

Multiply Equation 2 by 2: 2(3x + 5y) = 2(14) becomes 6x + 10y = 28

2. Now, subtract the equation (6x + 10y = 28) from (6x + 12y = 30) to eliminate 'x':

(6x + 12y) - (6x + 10y) = 30 - 28

6x - 6x + 12y - 10y = 2

2y = 2

y = 1

3. Substitute the value of 'y' (which we found to be 1) back into either of the original equations. Let's use the first equation:

2x + 4y = 10

2x + 4(1) = 10

2x + 4 = 10

2x = 10 - 4

2x = 6

x = 6/2

x = 3

Therefore, the solution to the given system of equations is x = 3 and y =1.

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Answer:i dont knowcan you tell me

Step-by-step explanation:

The give differential dy . y = tan x dy is incorrect an the correct one is dy = [dy/dx * y - sec^2(x) * dy/dx] / (dy/dx - tan(x))

To find the correct differential, we need to use the product rule of differentiation.

Starting with the given equation:

dy/dx * y = tan(x) * dy/dx

Now, we can use the product rule:

d/dx [ y * dy/dx ] = d/dx [ tan(x) * dy/dx ]

Using the chain rule on the right side:

d/dx [ y * dy/dx ] = sec^2(x) * dy/dx + tan(x) * d^2y/dx^2

Simplifying:

dy/dx * d/dy [y] + d^2y/dx^2 = sec^2(x) * dy/dx + tan(x) * d^2y/dx^2

Rearranging and factoring out the common factor of d^2y/dx^2:

(dy/dx - tan(x)) * d^2y/dx^2 = dy/dx * y - sec^2(x) * dy/dx

Finally, solving for the differential dy:

dy = [dy/dx * y - sec^2(x) * dy/dx] / (dy/dx - tan(x))

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Direct deposit is an electronic payment transfer that allows an employer to deposit an employee's pay check directly into their bank account. Hope's pay check is required to determine how much her employer deposited into her account on the most recent payday of 5/21/18.

The amount of the deposit depends on the employee's gross pay, which is the total amount of money earned before taxes and deductions are taken out. It is typically paid on a regular schedule, such as weekly or biweekly, depending on the employer. It is important for employees to keep track of their pay stubs and monitor their bank accounts to ensure that they are being paid accurately and on time.

So, it is required to check the bank account statement or Hope's pay check directly to determine the amount in her account on the most recent payday.

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Answer:

I think the answer is Associative.

Step-by-step explanation:

That's Commutative (a + b = b + a)

I hope Can to Help You ^_^

The third-order polynomial is: f(x) = 15 - 0.00125(x-15)² + 1.3889 x 10^-5(x-15)³

The third-order polynomial interpolation method can be used to plan the path given that the linear axis takes 3 seconds to move from Xo=15 mm to X-95 mm.

The following steps can be taken to plan the path:

Step 1:  Write down the data in a table as follows:

X (mm) t (s)15 0.095 1.030 2.065 3.0

Step 2: Calculate the coefficients for the third-order polynomial using the following equation:

f(x) = a0 + a1x + a2x² + a3x³

We can use the following equations to calculate the coefficients:

a0 = f(Xo) = 15

a1 = f'(Xo) = 0

a2 = (3(X-Xo)² - 2(X-Xo)³)/(t²)

a3 = (2(X-Xo)³ - 3(X-Xo)²t)/(t³)

We need to calculate the coefficients for X= -95 mm. So, Xo= 15mm and t= 3s.

Substituting the values, we get:

a0 = 15

a1 = 0

a2 = -0.00125

a3 = 1.3889 x 10^-5

Thus, the third-order polynomial is:f(x) = 15 - 0.00125(x-15)² + 1.3889 x 10^-5(x-15)³

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The value of x is  x€ {( x1=- 3/4+(√151)/4 i), (- 3/4  - (√151)/4 i)}

2X^2 + 3X + 20 = 0

Here we will use the Quadratic formula:

Once in standard form, identify a,b and c from the original equation and plug them into the quadratic formula.

2x∧2+ 3x +20=0

Give:

Here,

a= 2

b= 3

c= 20

x= (-3±√(3^2-4.2.20))/2a

x= (-3±√(3^2-4.2.20))/2.2

x= (-3±√(9-160))/(      2^(1+1) )

Now take x1 and x2 , as we have two signs + and -.

x1  = (-3+√(9-160))/(      2^2 )

x2   =   (-3-√(9-160))/(      2^2 )

x1  = (-3+√(-151))/(      2^2 )

x2  = (-3-√(-151))/(      2^2 )

x1   =   (-3+√(-151).  √(-1))/(      2^2 )  

x2   =   (-3-√(-151).  √(-1))/(      2^2 )

x1   =   (-3+√151.  i)/(      2^2 )  

x2   =   (-3-√151.  i)/(      2^2 )

x1   =   (-3+√151.  i)/(      4)  

x2   =  - (3+√151.  i)/(      4)

x1= - 3/4+(√151)/4 i

x2= - 3/4  - (√151)/4 i

x€ {( x1=- 3/4+(√151)/4 i), (- 3/4  - (√151)/4 i)}

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Answer:

5/16

Step-by-step explanation:

20/76=5/16

(Probability of individual accounting for the whole)

OR

The experimental probability is found by dividing the number of times the desired outcome occurred by the total number of trials. In this case, the desired outcome is selling a slice of pepperoni pizza as the first slice tomorrow.

Since we only know the number of slices sold today, we don't have any specific information about the number of slices that will be sold tomorrow. However, we can assume that the same types of pizzas will be sold tomorrow, and the probability of selling a slice of pepperoni pizza tomorrow will be the same as the proportion of pepperoni slices sold today.

So, the experimental probability that the first slice sold during lunch tomorrow will be a slice of pepperoni pizza is

Experimental probability = Number of pepperoni slices sold today / Total number of slices sold today

Experimental probability = 20 / 76

Experimental probability = 0.263

Answer:

5/19

Step-by-step explanation:

P(pepperoni)

=

pepperoni

total

=

20

76

=

5

19

So, P(pepperoni)=

5

19

.

Answer:

what do the lines look like

Step-by-step explanation:

Answer:

14 miles

Step-by-step explanation:

make it into an equation 1.50x+3=24 then solve

Answer:

14

Step-by-step explanation:

Answer:

b = 14

Step-by-step explanation:

In order to find the y intercept of the problem, we will have to put the equation of the line in point slope form and solve for y.

Point slope form: \(y-y_1=m(x-x_1)\)

Lets put the equation of the line in point slope form.

\(y-2=4(x+3)\)

Distribute 4

\(y-2=4x+12\)

Add 2 to both sides

\(y=4x+14\)

Now that the equation of the line is in slope intercept form, the y intercept is at the end of the equation, which is 14.

b = 14

The two non negative real numbers with a sum of 60 that have the largest possible​ product are 30 and 30.

What are non negative numbers?

Non-negative numbers are those that are either zero or positive (remember that 0 and 0 are the same). An integer that is either positive or zero is considered a non-negative integer. It is the result of adding all the natural numbers together with zero. It can be defined as the set "0, 1, 2, 3,...," and is also known as Z.

An integer that is either positive or zero is considered a non-negative integer.

Let us assume the two non negative numbers are \(x\) and \(y\).

According to the question,

Sum of two non negative numbers = 60

⇒ \(x+y=60\)

⇒ \(y=60-x\)

Their product will be given as,

⇒ \(P=xy\)

⇒ \(P=x(60-x)\)

⇒ \(P=60x-x^2\)

For the product to be largest \(P'(x)=0\)

⇒ \(P'(x) = 60-2x\)

⇒ \(60-2x=0\)

⇒ \(2x=60\)

⇒ \(x=30\)

Now, for the value of \(y\)

⇒ \(y=60-x\)

⇒ \(y=60-30\)

⇒ \(y=30\)

Therefore, the two non negative numbers are 30, 30.

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Step-by-step explanation:

in such problems with just equations we always need to have the main (optimization) equation or condition, and then usually some constraint equations.

the constant equations allow us typically to express one variable through another, until we have only one variable for the optimization equation. then we find the zeros of the first derivative of that functions and find the needed maximum or minimum if needed via the second derivative.

now if we have inequalities, it is even easier, I think.

we find the corners of the shaded area that must contain our minimum or maximum by finding the intersections of the delimiter lines. the optimum must be one of the corners.

and then we try the coordinates of the different corners in the optimization equation and see, which one delivers the highest or lowest value. and we are done.

a.

x + y <= 240

y >= 4x

b.

500x + 450y = profit

theoretically we have 3 corners to test

(0, 0)

(0, 240)

(48, 192)

(0, 0) is clearly the minimum, profit 0.

(0, 240) gives

450×240 = $108,000

(48, 192) gives

500×48 + 450×192 = 24000 + 86400 = $110,400

that is the maximum.

so, the farmer makes the most profit under the given constraints, if he plants 48 acres corn and 192 acres sprouts.

Answer:

hope you can understand

Answer:

(3,-3)

Step-by-step explanation:

See attachment 1 for complete question

Required

The unexplored point

To properly understand my solution, I will make use of another attachment where each of the given points will be identified on the point grid [See attachment 2]

From the second attachment, all points in the shaded region have been explored.

Only (3,-3) has not been explored

Answer:

$75.50

Step-by-step explanation:

The area of the region consisting of all the points Charlyn can see during her walk is equal to, A = 4840 km.

Charlyn is walking around the boundary of square A, which is 55 km long, and she has a horizontal vision of 11 km.

So as she walks around the square of 55 km, let there be another square B which lies outside square A, which is created due to her 11 km field of vision.

length of sides of square B = 55+(2×11) which is equal to 77 km.

And as she walks around the square of 55 km, let there be yet another square C which lies inside square A, which is created due to her 11 km field of vision.

length of sides of square C = 55-(2×11) which is equal to 33 km.

The area that Charlyn can see throughout her walk is equal to,

A = Area of square B - Area of square C.

The area of square B = Side² = 77² = 5929.

The area of square C = Side² = 33² = 1089.

A = 5929 - 1089.

A = 4840 km.

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Answer:

n - 3 = 12

Step-by-step explanation:

Hope this helps :)

Answer:

n=15

Step-by-step explanation:

n-3=12

Add 3 to both sides.

n=15

HTH :)

constraints in mathematical modeling can be represented using equations or inequalities, as well as systems of equations and/or inequalities.

In mathematical modeling, constraints are conditions or limitations that restrict the possible values or solutions of a problem. They can be represented using equations or inequalities, as well as systems of equations and/or inequalities. The solutions to these constraints can then be interpreted as viable or non-viable options within the context of the model.

Here are a few examples to illustrate the representation of constraints and the interpretation of solutions:

Example 1: Production Constraints

Let's say we are modeling a production process where we have limited resources. We have a constraint that the total number of units produced cannot exceed 100. We can represent this constraint as an inequality:

x ≤ 100

where x represents the total number of units produced. The solution to this constraint would be any value of x that is less than or equal to 100. Any value greater than 100 would be a non-viable option within the context of the production process.

Example 2: Budget Constraints

Suppose we are creating a budget for a project and have a constraint that the total expenses cannot exceed $5000. We can represent this constraint as an equation:

x + y + z = 5000

where x, y, and z represent different expense categories. The solution to this constraint would be any combination of values for x, y, and z that sum up to 5000. Any combination that exceeds 5000 would be non-viable within the budget constraints.

Example 3: Optimization Problem

Consider an optimization problem where we want to maximize a certain objective function subject to certain constraints. For instance, suppose we want to maximize the area of a rectangular garden while having a fixed perimeter of 40 meters. We can represent this problem using equations and inequalities:

2x + 2y = 40 (perimeter constraint)

Area = x * y (objective function)

The solution to this problem would be the values of x and y that satisfy the perimeter constraint while maximizing the area. These solutions would be the viable options within the context of the garden design.

In summary, constraints in mathematical modeling can be represented using equations or inequalities, as well as systems of equations and/or inequalities. The solutions to these constraints represent the viable or non-viable options within the context of the model, and they help guide decision-making and problem-solving processes.

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16 students should be sampled.

Using the z-distribution, it is found that 16 students should be sampled.

The margin of error of a z-confidence interval is given by:

\($M=z \frac{\sigma}{\sqrt{n}}$\)

In which:

- z is the crltical value.

- \($\sigma$\) Is the population standard devlation.

- nis the sample size.

The flrst step is flnding the critical value, which is z with a p-value of \($\frac{1+a}{2}$\), In which\($\alpha$\)is the confldence level.

In this problem, \($\alpha=0.95$\), thus, z with a p-value of \($\frac{1+0.95}{2}=0.975$\), which means that it is z=1.96.

Estlmate of the standard deviation of\($\mathbf{2}$\), thus, \($\sigma=2$\).

We want the sample for a margln of error of 1 , thus, we have to solve for n when M=1

\($M=z \frac{\sigma}{\sqrt{n}}$\)

\($1=1.96 \frac{2}{\sqrt{n}}$\)

\($\sqrt{n}=1.96(2)$\)

\($(\sqrt{n})^2=[1.96(2)]^2$\)

n= 15.4

Rounding up:

16 students should be sampled.

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Hi there!

5.

Use the property:

\(\frac{x^a}{x^b} = x^{a - b}\)
Now, solve by variable.

\(\frac{x^2}{x} = x^{2 - 1} = x\\\\\frac{y^5}{y^4} = y^{5 - 4} = y\)

Rewrite:
\(= x * y * z^3 = \boxed{\text{ D. } xyz^3}}\)

6.

Solve the inside of the parenthesis, and each term separately.

Use the property:
\(x^0 = 1\)

\((7 + 3^2)^0 = 1 \\\\(8^0 + 3)^2 = (1 + 3)^2 = 4^2 = 16\\\\1 + 16 = \boxed{ \text{ C. } 17}\)

7.

Solve like above:
\((4 + 2^2)^0 = 1\\\\(7^0 + 4)^{-3} = (1 + 4)^{-3} = 5^{-3}\)

The negative exponent indicates taking the reciprocal. Using the property:
\(x^{-a} = \frac{1}{x^a}\)

Therefore:
\(5^{-3} = \frac{1}{5^3} = \boxed{ \text{ D. }\frac{1}{125}}\)

Answer:

It's suppose to stand for OH AH OA which is for sine, cosine, and tangent. Sine, opposite divide by hypotenuse, cosine adjacent divided by hypotenuse, and tangent, opposite divided by adjacent. I personally like SOHCAHTOA more since it actually has the S,C, and T before what it means

Step-by-step explanation:

someone else answered this already

Answer:

It depends if it can or can't

Step-by-step explanation:

Really if you study hard enough you can recall basically anything you learned / relearn it. It only works with some people though and you definitely can have a "mind blank" time.

Other names for constant of proportionality are constant ratio, constant rate, unit rate, variable constant, and even rate of change.

What do you mean by proportion?

A ratio is a mathematical comparison of two numbers. If two groups of given numbers increase or decrease in the same proportion, the proportions are said to be directly proportional to each other. The ratio is the symbol ":" or "=". Two ratios are said to be proportional if they are equal.

The constant of proportionality is the ratio of the so-called proportional relationship that relates two given values ​​to each other. Other names for constant of proportionality are constant ratio, constant rate, unit rate, variable constant, and even rate of change.

The constant of proportionality goes by many other names, but can be remembered as a constant value that defines the proportional relationship between two quantities. Also known as constant ratio, constant rate, unit rate, variable constant, or rate of change.

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Being 95% confident in a statistical problem means that 95% of all possible samples will produce confidence intervals that contain the true population parameter.

In other words, if we were to take many random samples of the same size from the same population and construct a confidence interval for each of them, we would expect that 95% of those intervals would contain the true population parameter. It is important to note that this does not mean there is a 95% chance that a specific interval contains the true parameter; rather, once the interval is constructed, it either contains the parameter or it does not. The confidence level refers to the long-term frequency of intervals that contain the parameter, not to the probability that any individual interval contains the parameter.

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Answer:

y - 10 = 4(x - 3)

Step-by-step explanation:

y2 - y1 / x2 - x1

10 - (-2) / 3 - 0

12 / 3

= 4

y - 10 = 4(x - 3)

Answer:

192

Step-by-step explanation:

1600 × 0.12 = 192

Answer:

21/8 or 2.625

Step-by-step explanation: