a)Miss Said's basic pay is $128. She earns$36 for overtime and receives a bonus of $18. What is her gross pay?
b) Mrs Hafar's gross pay is $203. She pays$54 in tax and $18 towards her pension. What is her net pay?​

This gives us the equation of the normal line passing through the point (1, 2, 1): r(t) = (1 + 3t, 2 + 2t, 1 + 3t)

To find the equations of the tangent plane and normal line to the surface xy + yz + zx = 5 at the point (1, 2, 1), we first need to determine the normal vector to the surface at that point.

The surface equation xy + yz + zx = 5 can be rewritten as f(x, y, z) = xy + yz + zx - 5 = 0. The gradient of f(x, y, z) will give us the normal vector.

∇f(x, y, z) = (∂f/∂x, ∂f/∂y, ∂f/∂z) = (y + z, x + z, x + y)

At the point (1, 2, 1), the normal vector is ∇f(1, 2, 1) = (2 + 1, 1 + 1, 1 + 2) = (3, 2, 3).

Now, we can write the equation of the tangent plane using the point-normal form: (x - 1, y - 2, z - 1) · (3, 2, 3) = 0

Expanding this equation gives us the equation of the tangent plane:

3(x - 1) + 2(y - 2) + 3(z - 1) = 0

Simplifying, we have: 3x + 2y + 3z = 14

To find the equation of the normal line, we can parametrize it with a parameter t: x = 1 + 3t

y = 2 + 2t

z = 1 + 3t

This gives us the equation of the normal line passing through the point (1, 2, 1): r(t) = (1 + 3t, 2 + 2t, 1 + 3t)

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Answer:

That incorrect

Step-by-step explanation:

Yes

a) The probability histogram of pmf for the number of students who show up for a professor's office hour on a particular day is shown below.

b) The probability that at least two students show up = 0.55 and the probability that more than two students show up = 0.25

c) The probability that between one and three students show up = 0.7

d) The probability that the professor shows up = 0.20

First we write the number of students who show up for a professor's office hour on a particular day and their pmf in tabular form.

x        p(x)

0       0.20

1       0.25

2       0.30

3       0.15

4       0.10

The probability histogram of this data is shown below.

The probability that at least two students show up would be,

P(x ≥ 2) = p(2) + p(3) + p(4)

P(x ≥ 2) = 0.30 + 0.15 + 0.10

P(x ≥ 2) = 0.55

Now the probbability that more than two students show up:

P(x > 2) = p(3) + p(4)

P(x > 2) = 0.15 + 0.10

P(x > 2) = 0.25

The probability that between one and three students show up would be:

P(1 ≤ x ≤ 3) = p(1) + p(2) + p(3)

P(1 ≤ x ≤ 3) = 0.25 + 0.30 + 0.15

P(1 ≤ x ≤ 3) = 0.7

And the probability that the professor shows up would be: p = 0.20

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To be honest I don't know❤️

The root of the equation sinx = 2x-3 is 0.8401 (approx).

Given equation is sinx = 2x-3

We need to solve this equation using false position method.

False position method is also known as the regula falsi method.

It is an iterative method used to solve nonlinear equations.

The method is based on the intermediate value theorem.

False position method is a modified version of the bisection method.

The following steps are followed to solve the given equation using the false position method:

1. We will take the end points of the interval a and b in such a way that f(a) and f(b) have opposite signs.

Here, f(x) = sinx - 2x + 3.

2. Calculate the value of c using the following formula: c = [(a*f(b)) - (b*f(a))] / (f(b) - f(a))

3. Evaluate the function at point c and find the sign of f(c).

4. If f(c) is positive, then the root lies between a and c. So, we replace b with c. If f(c) is negative, then the root lies between c and b. So, we replace a with c.

5. Repeat the steps 2 to 4 until we obtain the required accuracy.

Let's solve the given equation using the false position method.

We will take a = 0 and b = 1 because f(0) = 3 and f(1) = -0.1585 have opposite signs.

So, the root lies between 0 and 1.

The calculation is shown in the attached image below.

Therefore, the root of the equation sinx = 2x-3 is 0.8401 (approx).

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0.636  is the probability that the ball chosen from urn .

What is probability ?

Urn A contains 2 W, 4 R

Urn B contains 8 W, 4 R

Urn C contains 1 W,  3 R

Probability of selecting 3 balls out of which 2 are white

P(J)=P(WWR)+P(WRW)+P(RWW)

      = 2/6 * 8/12 * 3/4 + 2/6 * 4/12 * 1/4 + 4/6 * 8/12 * 1/4 = 88/288

  Probability that the ball chosen from Urn A was white given that exactly 2 white balls  were selected

  P(A/J) = P(A ∩ J)/P(J)

            = 56/288/88/288

             = 0.636

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Answer:

(6,-1)

Step-by-step explanation:

(2, 1) is the first point,

(6, 1) is the point after it is reflected over x = 4,

(6, -1) is the point after it is reflected over the x-axis.

Answer:

1. 37°

2. 54°

3. 84°

Step-by-step explanation:

1. 180-(66+77)=37°

2. 180-(90+36)=54°

3. 360- (144+84+48)

Answer:

6.71

Step-by-step explanation:

The solution should be $6.71 because when you subtract $7.50 and $0.79 you end up with $6.71.

Answer:

3.25

Step-by-step explanation:

Answer:

3, 4, 5

Step-by-step explanation:

3² + 4² = 5²

=> 9 + 16 = 25

=> 25 = 25

Answer:

Side 1: 6

Side 2: 8

Side 3: 10

6² + 8²

36 + 64

√100 = 10

Side 1: 3

Side 2: 4

Side 3: 5

3² + 4²

9 + 16

√25 = 5

The sum of the square of the base and height should be equal to the square of the third number.

The expectation is -$9.6

Probability is the branch of mathematics concerning numerical descriptions of how likely an event is to occur, or how likely it is that a proposition is true.

Given that, a lottery offers one $1000 prize, two $700 prizes, three $300 prizes, and four $200 prizes.

Expected winning per ticket :

Σ(X × p(X)) = [(1000 × 1/1000) + (600 × 2/1000) + (300 × 2/1000) + (200 × 5/1000) - price per ticket

= 1 + 1.2 + 0.6 + 1 - 7

= 3.8-7

= -$3.2

Expected winning if 3 tickets are purchased :

3 × (-3.2) = -$9.6

Hence, the expectation is -$9.6

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Math is considered to have a sequential learning pattern because concepts and skills are introduced in a specific order, building upon previously learned material.

In math, concepts and skills are typically organized in a sequential manner, where each new topic builds upon what has been previously learned. This sequential learning pattern allows students to develop a solid foundation and gradually progress to more advanced topics.

For example, in elementary school, students first learn basic arithmetic operations like addition and subtraction before moving on to multiplication and division. These foundational skills are essential for understanding more complex mathematical concepts later on, such as algebra, geometry, and calculus. By following a sequential learning pattern, students can gradually develop their mathematical understanding and problem-solving abilities. They are able to connect new concepts to what they have already learned, reinforcing their knowledge and enabling them to apply it in different contexts. This sequential approach also ensures that students have the necessary prerequisite knowledge and skills to comprehend more advanced mathematical concepts. It helps create a logical progression in mathematical education, allowing students to build upon their previous knowledge and continually expand their mathematical abilities.

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Answer:

-24

Step-by-step explanation:

-7 +3 is -4

-4+-20 is -24

-7 + 3 - 20

= -4 - 20

= -4 + -20

= -24

______

Hope it helps ⚜

Answer:

r = radius of circle

Step-by-step explanation:

The circumference of a circle is given by :

C = 2πr

Where

r is the radius of the circle

In this problem, we need to say that what does r represents in the given formula. It means we can say that r stands for the radius of the circle.

Answer:

Step-by-step explanation:

..................

The difference in value between the two accounts after 8 years is approximately £18.01, with the Central Alliance Bank (CAB) account having a higher value.

For Central Alliance Bank (CAB) with simple interest, the formula to calculate the final amount (A) is:

A = P * (1 + r*t)

Let's calculate the final amounts for each account after 8 years:

Northern Savings Bank (NSB):

P = £6400

r = 2.5% = 0.025 (as a decimal)

n = 1 (compounded annually)

t = 8

A_NSB = £6400 * (1 + 0.025/1)^(1*8)

= £6400 * (1 + 0.025)⁸

= £6400 * (1.025)⁸

= £6400 * 1.20973297

≈ £7758.39

Central Alliance Bank (CAB):

P = £6400

r = 2.7% = 0.027 (as a decimal)

t = 8

A_CAB = £6400 * (1 + 0.027 * 8)

= £6400 * (1 + 0.216)

= £6400 * 1.216

≈ £7776.40

The difference in value between the two accounts after 8 years is:

Difference = A_CAB - A_NSB

= £7776.40 - £7758.39

≈ £18.01

Therefore, the difference in value between the two accounts after 8 years is approximately £18.01, with the Central Alliance Bank (CAB) account having a higher value.

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The height of the rectangle is 3.1 kilometers.

A rectangle is a 2-dimensional quadrilateral with four right angles and two diagonals which bisect each other . The perimeter of a rectangle is the distance round the rectangle. It is the sum of the four sides of the rectangle.

Perimeter of a rectangle = 2 x (height + width)

38.6 = 2 x (16.2 + height)

In order to determine the height, take the following steps:

38.6 / 2 = 16.2 + height

19.3 = 16.2 + height

height = 19.3 - 16.2 = 3.1 kilometers

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The missing values of the proportion are;

a. 18

b. 19.5

c. 45%

d. 180

The percentage of a number can be defined as the fraction of a number and hundred.

It is represented with the symbol, %.

From the information given, we have that'

1. 6% of 30

This is represented as;

60 /100 × 30

Multiply the values

18

2. 65% of 30

This is represented as

65/100 × 30

Multiply the values

1950/100

19.5

3. 18/40 × 100

Multiply the values

1800/40

45%

4. 81 = 45/100x

cross multiply the values

x = 180

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Answer:

2nd

1st

3rd

is the answers

The two given sides are identical, both are 6. This means the two bottom angles are also the same. Since angle E is given as 28, angle G would also be 28

The answer is A. 28

In the vapor-compression cycle, the working fluid (refrigerant) should contain only a liquid phase following the throttle valve operation.

The vapor-compression cycle is a common refrigeration cycle used in air conditioners, heat pumps, and refrigeration systems. It consists of four main components: compressor, condenser, throttle valve (also known as an expansion valve or metering device), and evaporator.

During the operation of the cycle, the working fluid undergoes phase changes between liquid and vapor states. The compressor increases the pressure and temperature of the refrigerant vapor, converting it into a high-pressure, high-temperature gas. This gas then enters the condenser, where it releases heat to the surroundings and condenses into a high-pressure liquid.

The liquid refrigerant then passes through the throttle valve, which acts as a restriction in the system. The purpose of the throttle valve is to reduce the pressure and temperature of the refrigerant, causing it to undergo a phase change. As a result, the refrigerant exits the throttle valve as a mixture of liquid and vapor, with a significant portion in the liquid phase.

After passing through the throttle valve, the refrigerant enters the evaporator. In the evaporator, heat is absorbed from the surroundings (such as the air in an air conditioning system) causing the remaining liquid refrigerant to evaporate, transforming into a low-pressure vapor.

Therefore, it is after the throttle valve operation that the working fluid (refrigerant) should ideally contain only a liquid phase. This ensures that the refrigerant enters the evaporator in its liquid state, facilitating the heat absorption process in the evaporator.

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By using the concept of differential equation, it can be calculated that

\(\\\begin{bmatrix} 3c_1e^{2t} +c_2e^{-5t} \\2c_1e^{2t} +3c_2e^{-5t} \end{bmatrix}\) is the general solution

What is a differential equation?

A differential equation is an equation consisting of one or more unknown variables and their derivative.

This is a problem on differential equation

\(x^{'} = \begin{bmatrix} 4 & -3 \\ 6 & -7\end{bmatrix}x\), \(x_1 = \begin{bmatrix} 3e^{2t} \\ 2e^{2t} \end{bmatrix}\), \(x_2 = \begin{bmatrix} e^{-5t}\\3e^{-5t}\end{bmatrix}\)

To show \(x_1 = \begin{bmatrix} 3e^{2t} \\ 2e^{2t} \end{bmatrix}\) is a solution of \(x^{'} = \begin{bmatrix} 4 & -3 \\ 6 & -7\end{bmatrix}x\)

\(x_1 = \begin{bmatrix} 3e^{2t} \\ 2e^{2t} \end{bmatrix}\\\\x_1^{'} = \begin{bmatrix} \frac{d}{dt}(3e^{2t}) \\ \frac{d}{dt}(2e^{2t})\end{bmatrix}\\\\x_1^{'} = \begin{bmatrix} 6e^{2t} \\ 4e^{2t}\end{bmatrix}\\\\ \begin{bmatrix} 4 & -3\\6 &-7\end{bmatrix}\begin{bmatrix} 3e^{2t} \\ 2e^{2t} \end{bmatrix} \\\\\begin{bmatrix} 12e^{2t}-6e^{2t} \\ 18e^{2t}-4e^{2t}\end{bmatrix}\\\\ = \begin{bmatrix} 6e^{2t} \\ 4e^{2t}\end{bmatrix}\)

So,  \(x_1 = \begin{bmatrix} 3e^{2t} \\ 2e^{2t} \end{bmatrix}\) is a solution of \(x^{'} = \begin{bmatrix} 4 & -3 \\ 6 & -7\end{bmatrix}x\)

To show \(x_2 = \begin{bmatrix} e^{-5t} \\ 3e^{-5t} \end{bmatrix}\) is a solution of \(x^{'} = \begin{bmatrix} 4 & -3 \\ 6 & -7\end{bmatrix}x\)

\(x_2 = \begin{bmatrix} e^{-5t} \\ 3e^{-5t} \end{bmatrix}\\\\x_2^{'} = \begin{bmatrix} \frac{d}{dt}(e^{-5t}) \\ \frac{d}{dt}(3e^{-5t})\end{bmatrix}\\\\x_1^{'} = \begin{bmatrix} -5e^{-5t} \\ -15e^{-5t}\end{bmatrix}\\\\ \begin{bmatrix} 4 & -3\\6 &-7\end{bmatrix}\begin{bmatrix} e^{-5t} \\ 3e^{-5t} \end{bmatrix} \\\\\begin{bmatrix} 4e^{-5t}-9e^{-5t} \\ 6e^{-5t}-21e^{-5t}\end{bmatrix}\\\\ = \begin{bmatrix} -5e^{-5t} \\ -15e^{-5t}\end{bmatrix}\)

So,  \(x_2 = \begin{bmatrix} e^{-5t} \\ 3e^{-5t} \end{bmatrix}\) is a solution of \(x^{'} = \begin{bmatrix} 4 & -3 \\ 6 & -7\end{bmatrix}x\)

W=

\(\begin{vmatrix} 3e^{2t} & e^{-5t} \\ 2e^{2t} & 3e^{-5t} \end{vmatrix}\\=9e^{-10t} - 2e^{-10t}\\=7e^{-10t}\\\neq 0\)

\(x_1\) and \(x_2\) are linearly independent

The general solution is

\(c_1x_1+c_2x_2\\c_1\begin{bmatrix} 3e^{2t} \\ 2e^{2t} \end{bmatrix} +c_2\begin{bmatrix} e^{-5t} \\ 3e^{-5t} \end{bmatrix}\\\begin{bmatrix} 3c_1e^{2t} +c_2e^{-5t} \\2c_1e^{2t} +3c_2e^{-5t} \end{bmatrix}\)

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Complete Question

The differential equation has been attached below

skewed left, median, 9

Step-by-step explanation:

edmentum

The first blank is skewed left, the second blank is median, and the third blank is 9 is correct options.

We have given that,

The shape of Gretchen's data can be described as ___ Because of this, the ___ be the best measure of center for this data set.

The actual value for the best measure of center is ___.

We have to determine the word in blank from the given diagram.

A left-skewed distribution has a long left tail. Left-skewed distributions are also called negatively-skewed distributions. That's because there is a long tail in the negative direction on the number line. The mean is also to the left of the peak. A right-skewed distribution has a long right tail.

Therefore the correct options are,

The first blank is skewed left, the second blank is median,and third blank is 9.

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Answer:

11y + 7

Step-by-step explanation:

4y + 5 + 2 + 7y

4y + 7y + 5 + 2 <== combine the like terms

11y + 7

Hope this helps!

Answer:

11y+7

Step-by-step explanation:

4y+5+2+7y

combine like terms

5+2=7

then you have

4y+7+7y

combine the y's

4y+7y=11y

then you got

11y+7  

Answer:

Number 7: 22.10 divided by 2.6 = 8.5  or 8.50 (depending on what your teacher prefers.

Step-by-step explanation:

Not sure about question 2 or 10