Which linear equation has a slope of 3 and a y-intercept of –2?
y = 3x + 2
y = 3x – 2
y = –2x + 3
y = –2x – 3

Answer:

from left to right

-8

-9

-10

-11

1. No span R³

2. No span R³

3. Span R³.

4. The matrices are linearly independent.

5. The matrices are linearly dependent.

6. The matrices are linearly independent.

1. {-3, 27, 3}, {-27, -1, 7}:

To determine if these vectors span R³, we check if the vectors are linearly independent. If they are linearly independent, they span R³; otherwise, they do not.

By calculating the determinant of the matrix formed by these vectors, we get:

|-3  27   3|

|-27 -1   7|

The determinant is zero, indicating that the vectors are linearly dependent.

Therefore, they do not span R³.

2. {3, 9, 5}, {42, -42, 11}:

The determinant is also zero, meaning the vectors are linearly dependent and do not span R³.

3. {-2 -5, 6, 15}, {4 -12, 12, 6}, {3, 3, 0}:

The determinant is non-zero, indicating that these vectors are linearly independent. Thus, they span R³.

1. S = {[1, 1], [2, 9]}, [4, -12], [12, 6], [3, 3]:

The determinant is non-zero, so the matrices are linearly independent.

2. S = {[1, -27], [22, -2]}, [4, -1], [4, 10], [16, -1], [0, 4]:

The determinant is non-zero, indicating that these matrices are linearly independent.

3. S = {[17, -27], [12, 12]}, [-5, -5], [-2, -2], [15, -31], [3, π], [0, e²]:

The determinant is zero, indicating that these matrices are linearly dependent.

4. S = {[4, -1], [4, -2]}, [16, -1], [4, 10], [10, -24], [-1, 0]:

The determinant is non-zero, indicating that these matrices are linearly independent.

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Answer:

y=-2/3x

I think that's the simplest form

a.  The sample size must be at least 8 to have a 95% confidence interval estimate for the gain in a circuit on a semiconductor device with a length of not greater than 60. b. The sample size must be at least 22 to have a 99% confidence interval estimate for the gain in a circuit on a semiconductor device with a length of not greater than 60.

a. The formula for finding the width of a confidence interval is:
Width of confidence interval = 2 × Zα/2 × σ/√n

where Zα/2 is the Z-score for the desired level of confidence.

For 95% confidence level, Zα/2 = 1.96.

Width of 95% confidence interval = 60σ = 30Zα/2 = 1.96

Substituting the given values in the formula:60 = 2 × 1.96 × 30/√nn = (2 × 1.96 × 30/60)²n = 7.84≈ 8

Therefore, the sample size must be at least 8 to have a 95% confidence interval estimate for the gain in a circuit on a semiconductor device with a length of not greater than 60.

b. For a 99% confidence level, Zα/2 = 2.576

Width of 99% confidence interval = 60σ = 30Zα/2 = 2.576

Substituting the given values in the formula:

60 = 2 × 2.576 × 30/√nn = (2 × 2.576 × 30/60)²n = 21.16≈ 22

Therefore, the sample size must be at least 22 to have a 99% confidence interval estimate for the gain in a circuit on a semiconductor device with a length of not greater than 60.

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Answer: No the triangle with sides 8cm 16 cm 18cm can't be a right angle triangle because of the Pythagoras theorem which states   that the square on the hypotenuse of a right-angled triangle is equal in area to the sum of the squares on the other two sides.

Step-by-step explanation:

Hope this was helpful

Answer:

no it is not a right angled triangle the Pythagoras theorem

To draw a vector starting at black dot 3, consider its location and orientation, consider vector V 2v→2, draw a vector in the same direction as V 2v→2, and double-check accuracy and grading criteria.

To draw the vector starting at the black dot 3, you need to consider the location and orientation. The exact length of the vector will not be graded, but the length relative to vector V 2v→2 will be graded.

Here's how you can draw the vector:

1. Start by locating the black dot 3 on your coordinate plane.
2. Determine the direction and orientation of the vector based on the given information.
3. Consider vector V 2v→2 and its length.
4. Draw a vector starting at black dot 3 that is in the same direction as V 2v→2. Remember, the length of this vector is not important, but its relative length compared to V 2v→2 is graded.
5. Make sure the vector starts at black dot 3 and points in the same direction as V 2v→2.

Remember to double-check your work and ensure that the vector is accurate and meets the grading criteria.

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From the information given about the above matrix, the value of |J| is 16.

It is to be noted that a Matrix, is a set of numbers arranged in rows and columns so as to form a rectangular array.

Given that J = [-1428];

Hence, the determinant of the matrix J is:

|J| = |(-1 * 8) - (4 *2)]

|J|  = |-8 - 8|

|J|  = | 16|

|J| = 16

Therefore, the value of  |J|  is 16.

Note: The determinant is a scalar variable in mathematics that is a function of the elements of a square matrix. It enables the characterization of some properties of the matrix as well as the linear map represented by the matrix.

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Answer:

b

Step-by-step explanation:

Answer:

(p -3q )(p -3q  )

Step-by-step explanation:

p'2 - 6pq + 9q'2

(p -3q )(p -3q  )

find two values that add to give 6 and multiply to 9

p x p =p'2

-3q x p = -3pq   -3 x pq = -3pq    ...... -3pq - 3pq = -6pq

-3q x - 3q = 9q'2

The vendor sold 172 sodas and 58 hotdogs at the hockey game.

An equation of degree one is known as a linear equation.

A linear equation of two variables can be represented by ax + by = c.

let, the number of soda cans be 'x' and the number of hot dogs be 'y'.

So, From the given information x = 3y and the vendor sold a total of 232.

Therefore, x + y = 232.

3y + y = 232.

4y = 232.

y = 232/4.

y = 58.

So, He sold 58 hot dogs and 3×58 = 172 soda cans.

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Answer:

8b

Step-by-step explanation:

You can factor the b-term out since b-term exists for all terms in the expression. By factoring out, you are basically dividing the factored term off and put it outside of the bracket, thus:

\(\displaystyle{16b-8b=\left(16-8\right)b}\)

Then evaluate and simplify:

\(\displaystyle{\left(16-8\right)b=8\cdot b}\\\\\displaystyle{=8b}\)

The required inverse of the given function is expressed as \(y=\sqrt{\frac{x+10}{7} }\)

A relation between a collection of inputs and outputs is known as a function. A function is, to put it simply, a connection between inputs in which each input is connected to precisely one output. Each function has a range, codomain, and domain. The usual way to refer to a function is as f(x), where x is the input.

Replacing y with x

x = 7y² – 10

Making y the subject of the formula:

7y² = x+ 10

Dividing both sides by 7

7y²/7 = (x+10)/ 7

y² = (x+10)/ 7

Taking the square root of both sides

\(\sqrt{y^{2} } =\sqrt{\frac{x+10}{7} }\)

\(y=\sqrt{\frac{x+10}{7} }\)

Hence the required inverse of the given function is expressed as  \(y=\sqrt{\frac{x+10}{7} }\)

Complete question:

Which equation is the inverse of y = 7x² – 10

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The probability of selecting a six-person committee as per given condition is equal to 0.1623 or 16.23%.

To calculate the probability of selecting four Democrats

And two Republicans in a six-person committee from a city council consisting of five Democrats and six Republicans,

Use the concept of combinations.

The total number of ways to form a committee of six people from a council of eleven five Democrats and six Republicans is

Using combination formula,

C(n, k) = n! / (k! × (n - k)!)

where n is the total number of items and k is the number of items chosen.

Here, select four Democrats and two Republicans,

Number of ways to choose four Democrats from five

C(5, 4)

= 5! / (4! × (5 - 4)!)

= 5

Number of ways to choose two Republicans from six,

C(6, 2)

= 6! / (2! × (6 - 2)!)

= 15

To find the total number of ways to form the committee with four Democrats and two Republicans, multiply the two results,

Total number of ways

= C(5, 4) × C(6, 2)

= 5× 15

= 75

The total number of ways to form a committee of six people from the city council is,

Total number of ways

= C(11, 6)

= 11! / (6! × (11 - 6)!)

= 462

Finally, calculate the probability by dividing the favorable outcomes (75) by the total number of outcomes (462),

Probability

= 75 / 462

≈ 0.1623

Therefore, the probability of selecting a six-person committee with four Democrats and two Republicans is approximately 0.1623 or 16.23%.

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The graph of the equation -3x+y=6 is linear and is attached with the answer below.

A linear equation is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.

A graph is the representation of the data on the vertical and horizontal coordinates so we can see the trend of the data.

The given linear equation is -3x+y=6. When we plot the linear equation -3x+y=6 on the graph it will be a straight line and the x and y-intercepts are -2 and 6 respectively.

The graph of the linear equation is attached with the answer below.

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Answer:

The answer is w = 5.

Step-by-step explanation:

1) Divide both sides by -4.

\(w + 1 = \frac{ - 24}{ - 4} \)

2) Two negative numbers makes a positive.

\(w + 1 = \frac{24}{4} \)

3) Simplify 24/4 to 6.

\(w + 1 = 6\)

4) Subtract 1 from both sides.

\(w = 6 - 1\)

5) Simplify 6 - 1 to 5.

\(w = 5\)

Therefor, the answer is w = 5.

The quantity 1.0 mg/cm2 is the same as 1.0 x 10-4 kg/m2.

To convert from milligrams per square centimeter (mg/cm2) to kilograms per square meter (kg/m2), we need to use conversion factors to adjust the units. The given options represent different powers of 10 that can be used as conversion factors.

We know that 1 kilogram (kg) is equal to 1,000,000 milligrams (mg), and 1 meter (m) is equal to 100 centimeters (cm). Therefore, we can express the conversion factors as follows:

1 kg = 1,000,000 mg (1)

1 m2 = 10,000 cm2 (2)

To convert from mg/cm2 to kg/m2, we can combine these conversion factors:

1 mg/cm2 = (1 mg / 1 cm2) x (1 kg / 1,000,000 mg) x (10,000 cm2 / 1 m2)

Simplifying the expression, we have:

1 mg/cm2 = (1 / 1,000,000) kg/m2 = 1 x 10-6 kg/m2

Therefore, the quantity 1.0 mg/cm2 is the same as 1.0 x 10-6 kg/m2.

Among the given options, the value that matches the conversion is option A: 10-4

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Answer:

a) no roots not in LHP

b) 2 roots not in LHP

c) 2 roots not in the LHP

d) 2 roots not in the LHP

e) 2 roots not in LHP

Step-by-step explanation:

False. It is necessary to have a base case in all recursive algorithms.

A base case is a condition that stops the recursion process and returns a result. Every recursive algorithm must have a base case. The base case is the point at which the recursion will stop, and the function will begin to return the values from the call stack. The base case is necessary to stop the recursive algorithm from entering an infinite loop that will cause it to consume all available resources, resulting in a stack overflow error. If there is no base case, the algorithm will continue to call itself until the stack overflows, which will result in a runtime error.

In conclusion, a base case is essential in all recursive algorithms, and the lack of one can result in a stack overflow error.

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Probability is the branch of mathematics dealing with numerical descriptions of how likely a situation is to occur, or how likely it is that a proposition is true.

An expression for the probability of an event.

Probability of an event = Required number of event / Total number of possible events

Required number of events = 84

Total number of events = 320

Find the probability that both customers selected without replacement say service is poor.

customers say service is poor = 84 / 320

customer selected without saying service is poor= 83 / 319.

The final probability is: 84 ÷ 320 ×83 ÷ 319.

      = 6972 ÷ 201080

     = 1743 ÷ 25520

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Answer:

250,000e^0.013t, where t is the number of years since 2000. In what year will the population reach 450,000?

Answer:

there will only be one 3

Step-by-step explanation:

see cause the first 3 of both numbers are 2 but only the last one of both numbers are 3 .

Answer:

B, 49π ft²

Step-by-step explanation:

Formula: Area of Circle = r²π

Step 1:

Radius = Diameter/2

14/2 = 7

Step 2:

Find the area of the circle using the formula.

7²π = 49π

Answer: 49π ft²

its a x, x, x√2 special triangle

so x and y are 19 <--- answer

2 angles are 90 & 45 so the third angle must be 45

that means x and y are equal

Answer:

third side = 6

Step-by-step explanation:

Using Pythagoras' identity in the right triangle.

The square on the hypotenuse is equal to the sum of the squares on the other 2 sides.

let the third side be x , then

x² + 8² = 10²

x² + 64 = 100 ( subtract 64 from both sides )

x² = 36 ( take the square root of both sides )

x = \(\sqrt{36}\) = 6

Answer:

Rational

Step-by-step explanation:

A rational number is a number that can be expressed as the quotient or fraction p/q of two integers, a numerator p, and a non-zero denominator q.

Hope This Helps :)

Answer:

The last one.

Step-by-step explanation:

Answer:

37.4

Step-by-step explanation:

1.1.1 Short-term investment: An example of a short-term investment is investing in a 3-month Treasury bill. These are government-issued debt securities with a maturity of less than one year, providing a relatively low-risk investment option with a fixed interest rate.

1.1.2 Medium-term investment: A medium-term investment example is investing in a corporate bond with a maturity of 5 years. Corporate bonds offer a higher yield compared to government bonds, making them suitable for investors with a moderate risk appetite seeking stable income over a longer time horizon.

1.1.3 Long-term investment: An example of a long-term investment is investing in a diversified stock portfolio. Stocks represent ownership in a company and have the potential for higher returns over an extended period, although they also involve higher risk.

1.1.4 Fixed income: An example of a fixed income investment is purchasing a 10-year government bond. These bonds pay a fixed interest rate over the bond's duration, providing a predictable stream of income for the investor.

1.1.5 Fixed expense: A fixed expense example is paying a monthly mortgage payment. The mortgage payment remains constant throughout the loan term, typically spanning several years, and includes both the principal repayment and the interest charged by the lender.

1.1.1 Short-term investment: A short-term investment option is the 3-month Treasury bill. Treasury bills are considered low-risk investments issued by the government, and they offer a fixed interest rate that is determined through an auction process. Investors can purchase Treasury bills directly from the government or through a broker.

1.1.2 Medium-term investment: A medium-term investment example is investing in a corporate bond with a 5-year maturity. Corporate bonds are issued by companies to raise funds, and they pay a fixed interest rate to bondholders over the bond's duration. The bond's yield and risk profile depend on the creditworthiness of the issuing company.

1.1.3 Long-term investment: An example of a long-term investment is investing in a diversified stock portfolio. A diversified portfolio consists of a mix of stocks from different sectors and regions, spreading the risk across multiple companies. The goal is to achieve long-term capital appreciation and potentially earn dividends from the stocks held in the portfolio.

1.1.4 Fixed income: An example of a fixed income investment is purchasing a 10-year government bond. Government bonds are issued by national governments to finance their operations. The bond's interest rate is fixed at the time of issuance, and the investor receives periodic interest payments until the bond reaches maturity, at which point the principal amount is returned.

1.1.5 Fixed expense: A fixed expense example is paying a monthly mortgage payment. When purchasing a property with a mortgage loan, the borrower agrees to make fixed monthly payments that include both the principal repayment and the interest charged by the lender. The monthly payment amount remains constant throughout the mortgage term, typically ranging from 15 to 30 years.

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(b) No, The branch manager's argument that dispatching buses every 0.5 minutes will reduce the average traveling time (a round trip) to 3.5 minutes is not correct.

To calculate the average time, we need to consider the time it takes for the bus to travel to the airport and back, as well as the time spent waiting for the bus.

If buses are dispatched every 3 minutes, and the average traveling time (a round trip) is 21 minutes, it means that passengers spend 18 minutes waiting for the bus (21 minutes - 3 minutes of traveling time).

If buses are dispatched every 0.5 minutes, the waiting time will be significantly reduced. However, the traveling time remains the same at 21 minutes for a round trip.

Therefore, the average traveling time will not be reduced to 3.5 minutes but will remain at 21 minutes (assuming the traveling time remains constant).

(c) The average traveling time, following the branch manager's suggestion of dispatching buses every 0.5 minutes, would still be 21 minutes.

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Complete question:

The Avis Company is a car rental company and is located three miles from the Los Angeles airport (LAX). Avis is dispatching a bus from its offices to the airport every 3 minutes. The average traveling time (a round trip) is 21 minutes.

(a) The branch manager wants to improve the service and suggests dispatching buses every 0.5 minute. She argues that this will reduce the average traveling time (a round trip) to 3.5 minutes. Is she correct? (Enter "Yes" or "No" in the following blank).

c. Following the branch manager's suggestion (dispatch busses every 0.5 min), what will the average traveling time be? average travelling time ____(mins) (enter the numbers only)