which of these is an example of a literal equation:

A: AX-BY=K

B: 5X+9Y

C: 4+12= 4²

D: 8-2X=14

Answer:

2x^2-4x+2

Step-by-step explanation:

depends what the question is telling you to do

if its askin you to simplify this is the answer

Answer and Step-by-step explanation:

For the first part

Tara is incorrect as she practices the softball in 4 days in a week and she do each practice of minimum one hour

So we can conclude that she practices minimum hours in a week  

For the second part

Also in 4 days, she does practice \(1 \frac{1}{3}\) hours per day i.e \(5 \frac{1}{3}\)

Now convert \(1 \frac{1}{3}\) this into a fraction which comes \(\frac{4}{3}\)

For four days, it is

= \(4 \times \frac{4}{3} \\\\ \frac{16}{3} \\\\ 5 \frac{1}{3}\)

Step-by-step explanation:

Without multiplying, explain how you know Tara is incorrect.

How long will Tara have softball practice this week? Write your answer as a mixed number.  

Each practice is \(1\frac{1}{3}\) hours

Each practice is more than 1 hour. so 4 days of practice is more than 4 hours.

So Tara is incorrect

Practice for 4 days

\(1\frac{1}{3}+1\frac{1}{3}+1\frac{1}{3}+1\frac{1}{3}=4\frac{4}{3}=5\frac{1}{3}\)

More than 5 hours .

Tara will have \(5\frac{1}{3}\) softball practice this week

Answer:

Tara will have \(5\frac{1}{3}\)  hours softball practice this week

Answer:

x= -6

Step-by-step explanation:

11=5-x

x=5-11

 =-6

Answer:

The diameter of horse hair is twice as thick as the diameter of the human hair.  

Step-by-step explanation:

The diameter of a human hair = \(6.5\times 10^{-4}\ \inches\)

The diameter of a horse hair = \(1.3\times 10^{-3}\ \inches\)

Dividing the diameter of a horse hair to the diameter of a human hair as follows :

\(\dfrac{\text{Diameter of human hair}}{\text{Diameter of horse hair}}=\dfrac{6.5\times 10^{-4}}{1.3\times 10^{-3}}\\\\\dfrac{\text{Diameter of human hair}}{\text{Diameter of horse hair}}=\dfrac{1}{2}\\\\\text{Diameter of horse hair}=2\times \text{Diameter of human hair}\)

So, the diameter of horse hair is twice as thick as the diameter of the human hair.  

Answer:

The horse hair is 2 times as thick as the human hair.

Step-by-step explanation:

<QPR=<PRS (BEING ALTERNATE ANGLE)

<PRS=65

THEN,

45+65+<SRT=180

<SRT=70

Investment in automation cost = $8,750,000 when there

no further change in capacity.

Every three-dimensional object occupies some space. This space is measured in terms of its volume. Volume is defined as the space occupied within the boundaries of an object in three-dimensional space. It is also known as the capacity of the object.

Following are the informations of Cent:

Current automation = 7%

Capacity of next round = 1,100

New automation = 7 + 2 = 9

Investment in automation cost = Capacity * (4 * (New automation - previous automation)) * 1000

= 1,100 * (4 * (9 - 7)) * 1,000

= 1,100 * (4 * 2) * 1000

= 1,100 * 8 * 1,000

= $8,800,000.

Investment in automation cost = $8,800,000.

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Step-by-step explanation:

-5x+2y= 4         <==== Multiply entire equation by -3 to get:

15x-6y = -12  

2x+3y= 6          <====  Multiply entire equation by 2 to get :

4x+6y = 12    Add the two underlined equations to eliminate 'y'

19x = 0     so x = 0

sub in x = 0 into any of the equations to find:  y = 2

(0,2)

Based on the given informations, the change in y as t changes from 1 to 6 is approximately 3.870. Therefore the correct option is (A).

To find the change in y as t changes from 1 to 6, we need to integrate the given function with respect to t over the interval [1, 6] and then find the difference between the values of the integral at the two endpoints.

∫₁⁶ 6e\(.^{(-0.08(t-5)^2)}\)  dt

We can use the substitution u = t - 5 to simplify the integral:

∫₋₄¹ 6e\(.^{(-0.08u^2)}\)  du

Unfortunately, there is no closed-form solution for this integral. We can use numerical integration methods, such as Simpson's rule or the trapezoidal rule, to approximate the integral. Using Simpson's rule with a step size of 1, we get:

∫₋₄¹ 6e\(.^{(-0.08u^2)}\) du ≈ 3.870

Therefore, the change in y as t changes from 1 to 6 is approximately 3.870, which corresponds to option (A).

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The value of x would be 1.

The probability of rolling exactly a 1 when a dice is picked randomly from two 4-sided dice and three 6-sided dice is 0.4 or 40%.

To calculate the probability of rolling exactly a 1 when a dice is picked randomly from two 4-sided dice and three 6-sided dice, we need to determine the total number of dice and the number of dice that have a 1 as a possible outcome.

There are two 4-sided dice and three 6-sided dice, so the total number of dice is 2 + 3 = 5.

Out of these five dice, we need to determine how many have a 1 as a possible outcome.

Among the two 4-sided dice, there is only one die (out of two) that has a 1 as a possible outcome.

Among the three 6-sided dice, there is also one die (out of three) that has a 1 as a possible outcome.

Therefore, there are a total of two dice that have a 1 as a possible outcome.

The probability of rolling exactly a 1 when a dice is picked randomly is calculated by dividing the number of favorable outcomes (two dice) by the total number of possible outcomes (five dice):

Probability = Number of favorable outcomes / Total number of possible outcomes

Probability = 2 / 5

Probability = 0.4

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Answer:

u =√6

v =√5

Step-by-step explanation:

u = √(1²+2²+1²) =√(1+4+1) = √6

v = √(1²+2²) =√(1+4) = √5

The possible lengths of the rectangular parking lot are any value less than or equal to 80 feet or any value greater than or equal to 110 feet, as long as the width is calculated accordingly to satisfy the given conditions of the perimeter and area.

The possible lengths of the rectangular parking lot can vary, but they must adhere to the conditions of having a perimeter of 380 feet and an area of at least 8800 square feet.

Let's assume the length of the parking lot is L and the width is W. The perimeter of a rectangle is given by the formula P = 2L + 2W. In this case, we are given that the perimeter is 380 feet, so we can write the equation as 2L + 2W = 380.

Additionally, the area of a rectangle is given by the formula A = L × W. We are given that the area must be at least 8800 square feet, so we can write the inequality as L × W ≥ 8800.

To determine the possible lengths of the parking lot, we can use these equations. First, let's solve the perimeter equation for W: W = (380 - 2L)/2 = 190 - L. Next, substitute this value of W into the area inequality equation: L × (190 - L) ≥ 8800.

Simplifying this inequality, we get L² - 190L + 8800 ≥ 0. To find the possible values of L, we can solve this quadratic inequality. By factoring or using the quadratic formula, we can determine that the possible lengths are L ≤ 80 or L ≥ 110.

Therefore, the possible lengths of the rectangular parking lot are any value less than or equal to 80 feet or any value greater than or equal to 110 feet, as long as the width is calculated accordingly to satisfy the given conditions of the perimeter and area.

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48+140=188

92+210=302

if you at all it equals 490

Step-by-step explanation:

(1) 4mn × 6mp × 3mnp

= 4 × 6 × 3 ( mn × mp × mnp)

= 72 × (m³n²p²)

72m³n²p²

sorry, I'm busy, won't be able to complete it

The determinant of the coefficient matrix of the given system is zero, indicating that the system does not have a unique solution.

The determinant of a matrix is a scalar value that provides important information about the matrix. In the given system, the coefficient matrix is:

[-3 0 -2]

[ 9 0 5]

[ 6 0 -12]

To find the determinant, we can use various methods, such as cofactor expansion or row reduction. In this case, we can simplify the matrix by performing row operations. Notice that the second row is three times the first row, and the third row is two times the first row. Therefore, the determinant of the coefficient matrix will be zero because the rows are linearly dependent.

When the determinant of a coefficient matrix is zero, it implies that the system of equations is dependent or inconsistent. Geometrically, the equations represent planes in three-dimensional space. A determinant of zero means that the planes are parallel or coincident, resulting in infinitely many solutions or no solution at all. In this case, the system is dependent, and the equations are not sufficient to determine a unique solution for the variables x, y, and z.

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Answer:

B.

Step-by-step explanation:

Answer: A. 95

Step-by-step explanation: The angles in a triangle are supposed to add up to 180 degrees, 55+30= 85 and 85+95 is 180.

The angle measures are;

m < 1  = 33°

m < 2 = 57°

It is important to note that complementary angles are defined as pairs of angles that sum up to 90 degrees.

From the information given, we have the angle measures as;

This can be represented as;

m < 1 + m < 2 = 90

Now, let's substitute the values into the equation, we have;

(x + 14) + 3x = 90

expand the bracket, we have;

x + 14 + 3x = 90

collect like terms

4x = 90 - 14

subtract the values

4x = 76

Make 'x' the subject of formula, we get;

x = 76/4

x = 19

Then,

m < 1 = (x + 14) = 19 + 14 = 33°

m < 2 = 3x = 3(19) = 57°

Hence, the values are 33° and 57° respectively.

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The complete question is;

In the figure below, m < 1 = (x + 14) and m < 2 = 3x, are both complementary to each other

Find the angle measures.

Answer:

t < 3.8 minutes

Step-by-step explanation:

We are told that the temperature "t" minutes after being cooled is

60(5/6)^t

We want to find After how many

minutes will the temperature of the solution be less than 30°C

Thus;

60(5/6)^t < 30

Divide both sides by 60 to get;

(5/6)^t < 0.5

t In(5/6) < In 0.5

-0.1823t < -0.6931

t < 0.6931/0.1823

t < 3.8 minutes

Answer:

x=1.5 y=-1/3

Step-by-step explanation:

2x-3y=4

2x+8=11

Let's subtract 8 from both sides of the second equation:

2x=3

x=1.5

Substituting this into the first equation, we get:

2(1.5)-3y=4

3-3y=4

-3y=1

y=-1/3

The probability of producing less than 239,000 barrels is 0.8413.

The probability of producing less than 239,000 barrels can be found using the z-score formula. The z-score formula is given by:
z = (x - μ) / σ
Where x is the value we are interested in, μ is the mean, and σ is the standard deviation.
Plugging in the given values, we get:
z = (239,000 - 232,000) / 7,000
z = 1
Now, we can use the standard normal table to find the probability of producing less than 239,000 barrels. The standard normal table gives the probability of a value being less than a given z-score. For a z-score of 1, the probability is 0.8413.
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(a) The set {(x1,x2)T|x1 + x2 = 0} is a subspace of R2.

To check whether the given set is a subspace of R2, we need to check whether it is closed under vector addition and scalar multiplication. Let u = (u1,u2)T and v = (v1,v2)T be two arbitrary vectors in the set, and let c be an arbitrary scalar. Then:

u + v = (u1 + v1, u2 + v2)

Since u1 + v1 + u2 + v2 = (u1 + u2) + (v1 + v2) = 0 + 0 = 0 (since u and v are in the set), we see that u + v is also in the set.

c*u = (c*u1, c*u2)

Since c*u1 + c*u2 = c*(u1 + u2) = c*0 = 0 (since u is in the set), we see that c*u is also in the set.

Therefore, the set {(x1,x2)T|x1 + x2 = 0} is a subspace of R2.

(b) It is not a subspace of R2

To check whether the given set is a subspace of R2, we need to check whether it is closed under vector addition and scalar multiplication.

Let u = (u1,u2)T and v = (v1,v2)T be two arbitrary vectors in the set, and let c be an arbitrary scalar. Then:

u + v = (u1 + v1, u2 + v2)

Since u21 = u22 and v21 = v22 (since u and v are in the set), we see that (u1 + v1)2 = (u2 + v2)2. Therefore, u + v is in the set.

c*u = (c*u1, c*u2)

Since u21 = u22 (since u is in the set), we see that (c*u1)2 = (c*u2)2. Therefore, c*u is in the set.

However, the set {(x1,x2)T|x21 = x22} is not a subspace of R2 because it does not contain the zero vector (0,0)T, which is required for any set to be a subspace.

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The derivatives of the given functions are:

h'(t) = 6.4t^(2.2) + 6.4t^(-4.2),

h'(3) = 6.4(3)^(2.2) + 6.4(3)^(-4.2),

h''(t) = 14.08t^(1.2) - 26.88t^(-5.2),

h''(3) = 14.08(3)^(1.2) - 26.88(3)^(-5.2),

f'(x) = (-119x^2 + 70x) / (49x^4),

f''(x) = (-117442x^5 + 68600x^4) / (2401x^8),

f'''(x) = (-27234673524x^12 + 158067736000x^11) / (5764801x^16).

To compute the derivatives of the given functions, we can use the power rule and constant rule of differentiation.

To find h'(t) (the first derivative of h(t)), we differentiate each term separately using the power rule:

h'(t) = 2 * 3.2 * t^(3.2 - 1) - 2 * (-3.2) * t^(-3.2 - 1)

= 6.4t^(2.2) + 6.4t^(-4.2).

To find h'(3), we substitute t = 3 into the expression for h'(t):

h'(3) = 6.4(3)^(2.2) + 6.4(3)^(-4.2).

To find h''(t) (the second derivative of h(t)), we differentiate h'(t):

h''(t) = 6.4 * 2.2 * t^(2.2 - 1) - 6.4 * 4.2 * t^(-4.2 - 1)

= 14.08t^(1.2) - 26.88t^(-5.2).

To find h''(3), we substitute t = 3 into the expression for h''(t):

h''(3) = 14.08(3)^(1.2) - 26.88(3)^(-5.2).

To find f'(x) (the first derivative of f(x)), we use the quotient rule:

f'(x) = [(7x^2)(-5) - (6 - 5x)(14x)] / (7x^2)^2

= (-35x^2 - 84x^2 + 70x) / (49x^4)

= (-119x^2 + 70x) / (49x^4).

To find f''(x) (the second derivative of f(x)), we differentiate f'(x):

f''(x) = [(-119x^2 + 70x)(98x^3) - (2(-119x^2 + 70x)(4x^3))] / (49x^4)^2

= (-117442x^5 + 68600x^4) / (2401x^8).

To find f'''(x) (the third derivative of f(x)), we differentiate f''(x):

f'''(x) = [(-117442x^5 + 68600x^4)(16807x^7) - ((-117442x^5 + 68600x^4)(3)(2401x^8))] / (2401x^8)^2

= (-27234673524x^12 + 158067736000x^11) / (5764801x^16).

Therefore, the calculations for the derivatives are:

h'(t) = 6.4t^(2.2) + 6.4t^(-4.2),

h'(3) = 6.4(3)^(2.2) + 6.4(3)^(-4.2),

h''(t) = 14.08t^(1.2) - 26.88t^(-5.2),

h''(3) = 14.08(3)^(1.2) - 26.88(3)^(-5.2),

f'(x) = (-119x^2 + 70x) / (49x^4),

f''(x) = (-117442x^5 + 68600x^4) / (2401x^8),

f'''(x) = (-27234673524x^12 + 158067736000x^11) / (5764801x^16).

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From the stem and leaf plot, let's write the data set:

10.9 cm

11.0 cm

11.2 cm

11.2 cm

12.1 cm

12.3 cm

We need to find the range of the data set, which is, the difference between the length of the longest pencil and the shortest pencil.

From the data set, we can see:

• Length of Longest Pencil = 12.3 cm

• Length of Shortest Pencil = 10.9 cm

The difference is

12.3 - 10.9 = 1.40 cm

Answer:

Megan's plant is 457 Inches tall

Step-by-step explanation:

ffggddaafvvcgghv de ryhvg

Form the given five quadratics , the one representing the repeated roots is equal to option d. 25x² - 30x + 9 and repeated roots are 3/5 or 3/5.

Quadratics representing repeated roots has discriminant equals to zero.

Standard quadratic equation is:

ax² + bx + c = 0

Discriminant 'D' = b² - 4ac

option a. -x²+ 18x + 81

Discriminant

'D' = 18² - 4(-1)(81)

      = 324 + 324

      = 648

D>0 has distinct roots.

option b. 3x²- 3x - 168

Discriminant

'D' = (-3)² - 4(-3)(-168)

      = 9 - 2016

      = -2007

D< 0 has distinct roots.

option c. x²- 4x -  4

Discriminant

'D' = (-4)² - 4(1)(-4)

      = 16 + 16

      = 32

D>0 has distinct roots.

option d. 25x²- 30x + 9

Discriminant

'D' = (-30)² - 4(25)(9)

      = 900 - 900

      = 0

D = 0 has repeated roots.

Repeated roots are:

x = ( -b ±√D ) / 2a

  = [-(-30)±√0 ]/ 2(25)

  = 30/ 50

  = 3/5.

option e.  x² - 14x + 24

Discriminant

'D' = (-14)² - 4(1)(24)

      = 196 - 96

      = 100

D>0 has distinct roots.

Therefore, the quadratics which represents the repeated roots are given by option d. 25x² - 30x + 9 and its repeated roots are 3/5 or 3/5.

The above question is incomplete, the complete question is:

One of the five quadratics below has a repeated root. (There other four have distinct roots.) What is the repeated root?

a. -x²+ 18x + 81

b. 3x² - 3x - 168

c. x² - 4x - 4

d. 25x² - 30x + 9

e. x² - 14x + 24

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The probability that the Davis boys will occupy the first two seats in the row, the Jones boys will occupy the next three seats, and the Smith boys will occupy the last four seats is 7.937×\(10^{-4}\).

There are \(\left[\begin{array}{ccc}9\\2,3,4\\\end{array}\right]\) potential arrangements for the nine boys if we do not make a distinction amongst boys with the same last name. We are curious in the likelihood of a specific one of these configurations.

Probability = \(\frac{1}{\left[\begin{array}{ccc}9\\2,3,4\\\end{array}\right]}\)

                  = \(\frac{2!3!4!}{9!}\)

                 = 0.0007937

                = 7.937×\(10^{-4}\)

Hence, the probability is 7.937×\(10^{-4}\).

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The correct answer is not listed in the options, so there might have been a mistake in the question or the choices provided. To find the fourth ordered pair using the two sequences, we need to apply each rule to the previous result, starting from the given starting points.

Using Rule 1, starting from 1:
- Multiply by 2: 1 x 2 = 2
- Add one third: 2 + (1/3) = 7/3
So the first term of the fourth ordered pair is 7/3.
Using Rule 2, starting from 0:
- Add one half: 0 + 1/2 = 1/2
- Multiply by 4: (1/2) x 4 = 2
So the second term of the fourth ordered pair is 2.
Therefore, the fourth ordered pair is (7/3, 2).

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