10c - cd + d (if c= -6 and d = 2)

If the first quartile is 39 years old, it means that approximately one-fourth of the employees at CCNHS – Main Campus are 39 years old or younger.

The first quartile (Q1) of the ages of the 256 employees of CCNHS – Main Campus being 39 years old implies that 25% of the employees have an age equal to or less than 39 years old.

In statistical terms, the first quartile represents the point below which 25% of the data falls. It divides the data set into four equal parts, with each part containing 25% of the data. Therefore, if the first quartile is 39 years old, it means that approximately one-fourth of the employees at CCNHS – Main Campus are 39 years old or younger.

This information provides insight into the age distribution of the employees at the institution. It indicates that a significant portion of the employees are relatively young, with a quarter of them falling below the age of 39. Understanding the age demographics of the workforce can be useful for various purposes, such as planning professional development programs or implementing age-specific policies.

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A graph which represent the function f(x) = 4/x is: A. on a coordinate plane, a hyperbola is shown. A curve opens up and to the right in quadrant 1, and another curve opens down and to the left in quadrant 3. A vertical asymptote is at x = 0.

In Mathematics, an asymptote can be defined as a line which the graph of a given function approaches but would never touch. Additionally, the vertical asymptote of a function refers to the value of x which makes its denominator equal to zero (0).

In order to graph a rational function, it is very important to determine the values for which it is undefined. Additionally, a function is said to be undefined when the value of its denominator is equal to zero (0), which represents the vertical asymptote lines.

f(x) = 4/x

y = 4/0 (undefined).

Therefore, the graph of x = 0 is a vertical asymptote.

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Answer:

that should be graph A on edge

Step-by-step explanation:

Answer: No solution

Step-by-step explanation:

-10x-16=14

-16x-6=14

-10x-16=-16x-6

-10x+16x-16=-16x+16x-6

6x-16=-6

6x-16+16=-6+16

6x=10

x=10/6

x=5/3

-16(5/3)-6=

-80/3-6*3/3=

-80/3-18/3=

(-80-18)/3=-98/3 \(\neq\) 14

Hence, there is no solution

The equation is proved.

G\(`tan(x-1)(sin2x-2cos2x)=2(1-2sinxcosx)`\)

We need to prove the given equation. Solution: Using the identity \(`sin2x=2sinxcosx` and `cos2x=1-2sin^2x`\)

in the given equation, we get

\(`tan(x-1)(sin2x-2cos2x)=2(1-2sinxcosx)`⟹ `tan(x-1)(2sinxcosx-2(1-\)

\(2sin^2x))=2(1-2sinxcosx)`⟹ `tan(x-1)(4sin^2x-2)=2-4sinxcosx`⟹ `2sin(x-1)\)

\((2sin^2x-1)=2(1-2sinxcosx)`⟹ `2sin(x-1)(2sin^2x-1)=2(1-2sinxcosx)`⟹\)

\(`2sinxcos(x-1)(4sin^2x-2)=2(1-2sinxcosx)`⟹ `2sinxcos(x-1)(2sin^2x-1)=1-\)

\(sinxcosx`⟹ `2sinxcos(x-1)(2sin^2x-1)=sin^2x+cos^2x-sinxcosx`⟹\)

`\(2sinxcos(x-1)(2sin^2x-1)=(sinx-cosx)^2`⟹ `sinxcos(x-1)(2sin^2x-1)=(sinx-cosx)^2/2`\)

For `LHS`, using identity

\(`sin(90 - x) = cosx`⟹ `sinxcos(x-1)(2sin^2x-1)=(sinx-sin(91-x))^2/2`⟹\)

\(`sinxcos(x-1)(2sin^2x-1)=(-sin(x-1))^2/2`⟹ `sinxcos(x-1)(2sin^2x-1)=sin^2(x-\)

\(1)/2`⟹ `sinxcos(x-1)(4sin^2x-2)=sin^2(x-1)`⟹ `sinxcos(x-1)(2sin^2x-1)=1/2`⟹ `1/2=1/2`.\)

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The general solution of the partial differential equation is:

U(x, t) = Σ [Aₙ*sin((nπ/3)x)]*e^(-(nπ/3)²t)

The partial differential equation (PDE) is given as:

Uxx = (1/2)Ut with the boundary and initial conditions as 0< X <3 with U(0,t) = U(3, t)=0, U(0, t) = 5sin(4πx)

Assume that the solution can be written as a product of two functions:

U(x, t) = X(x)T(t)

Substituting this into the PDE, we have:

X''(x)T(t) = (1/2)X(x)T'(t)

Dividing both sides by X(x)T(t), we get:

(X''(x))/X(x) = (1/2)(T'(t))/T(t)

Since the left side only depends on x and the right side only depends on t, both sides must be equal to a constant, denoted as -λ²:

(X''(x))/X(x) = -λ²

(1/2)(T'(t))/T(t) = -λ²

Simplifying the second equation, we have:

T'(t)/T(t) = -2λ²

Solving the second equation, we find:

T(t) = Ce^(-2λ²t)

Applying the boundary condition U(0, t) = 0, we have:

U(0, t) = X(0)T(t) = 0

Since T(t) ≠ 0, we must have X(0) = 0.

Applying the boundary condition U(3, t) = 0, we have:

U(3, t) = X(3)T(t) = 0

Again, since T(t) ≠ 0, we must have X(3) = 0.

Therefore, we can conclude that X(x) must satisfy the following boundary value problem:

X''(x)/X(x) = -λ²

X(0) = 0

X(3) = 0

The general solution to this ordinary differential equation is given by:

X(x) = Asin(λx) + Bcos(λx)

Applying the initial condition U(x, 0) = 5*sin(4πx), we have:

U(x, 0) = X(x)T(0) = X(x)C

Comparing this with the given initial condition, we can conclude that T(0) = C = 5.

Therefore, the complete solution for U(x, t) is given by:

U(x, t) = Σ [Aₙsin(λₙx) + Bₙcos(λₙx)]*e^(-2(λₙ)²t)

where:

Σ represents the summation over all values of n

λₙ are the eigenvalues obtained from solving the boundary value problem for X(x).

To find the eigenvalues λₙ, we substitute the boundary conditions into the general solution for X(x):

X(0) = 0: Aₙsin(0) + Bₙcos(0) = 0

X(3) = 0: Aₙsin(3λₙ) + Bₙcos(3λₙ) = 0

From the first equation, we have Bₙ = 0.

From the second equation, we have Aₙ*sin(3λₙ) = 0. Since Aₙ ≠ 0, we must have sin(3λₙ) = 0.

This implies that 3λₙ = nπ, where n is an integer.

Therefore, λₙ = (nπ)/3.

Substituting the eigenvalues into the general solution, we have:

U(x, t) = Σ [Aₙ*sin((nπ/3)x)]*e^(-(nπ/3)²t)

where Aₙ are the coefficients that can be determined from the initial condition.

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Answer:

0

Step-by-step explanation:

Distribute 6 to each variable inside the parenthesis.

6 ( x − x + 2 − 1 − 2 + 1 )

= 6x - 6x + 12 - 6 - 12 + 6

Combine like terms.

6x - 6x + 12 - 6 - 12 + 6

= 12 - 6 - 12 + 6

= 6 - 12 + 6

= -6 + 6

= 0

Answer:

Hello, the answer is 141.82

hope this helps

Step-by-step explanation:

Step-by-step explanation:

Slope 1/2    point    5,1  

  in point slope form would be

    (y-1) = 1/2 (x-5)

Answer:

In the fifth month the contestant must lose 6 pounds of weight.

Step-by-step explanation:

Given that the contestant wants to lose an average of 8 pounds of weight per month for 5 months, taking into account that in the first 4 months of the contest he lost 12, 9, 5 and 8 pounds respectively, to determine how much weight he should lose in the fifth month the following calculation must be performed:

8 x 5 = 40 (pounds to lose)

12 + 9 + 5 + 8 = 34 (pounds lost)

40 - 34 = 6

Therefore, in the fifth month the contestant must lose 6 pounds of weight.

The element which should be used to help clarify a complicated idea in a text is ; A research question.

According to the question;

A research question is the best fit which should be used to help clarify a complicated idea in a text.

This is so because; a research question provides a basis for accessing all perspectives there is to the complicated idea.

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Answer:

D:) a research question.

Step-by-step explanation:took the test

Answer:

4

Step-by-step explanation:

7 - (15 / 5)

7 - (3)

= 4

if you like my answer please mark me brainliest!! thanks <3

Answer:x=5

Step-by-step explanation:

2x-4=6 Then you at 4 to both sides

2x=10 Divide

x=5

Answer:

d = 359 + 344d

Step-by-step explanation:

d = 359 + 344d

By using the concept of control chart, it can be concluded that

A large number of plots are on or near the centerline.

Third option is correct.

What is control chart?

Control chart is used to show how a process changes over time.

There are three lines in a control chart.

They are the central line for the average, upper line for the Upper Control Limit (UCL) and a lower line for the Lower Control Limit (LCL)

It is known that the highest performance of a process is obtained when it is between the LCL and the UCL.

That means to get the best result, samples needs to be concentrated near the centerline.

So the third option is correct

A large number of plots are on or near the centerline.

Third option is correct.

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Complete Question

Quality control charts usually have a central line and upper and lower control limit lines. Which of the following is not a reason that the process being monitored with the chart should be investigated?

A sudden and sustained shift in the plots toward the upper or lower control limit

There is an upward trend in the plots

A large number of plots are on or near the central line

A single plot falls outside of the control limits

x = 11.8

y = 2.1

We apply the trigonometry ratio SOHCAHTOA

The hypotenuse = 12cm

adjacent = base = y

The opposite (side opposite the angle) = x

The angle = 80 degrees

To get x, we apply sine ratio (SOH)

sin 80 = opposite/hypotenuse

sin 80 = x/12

x = 12 × sin80

x = 12 = 0.9848

x = 11.8176

To the nearest tenth, x = 11.8

To get y, we apply cosine ratio (CAH)

cos80 = adjacent/hypotenuse

cos80 = y/12

y = ×12 cos80

y = × 12 0.1736

y = 2.0832

To the nearest tenth, y = 2.1

Answer:

B and E

Step-by-step explanation:

the graph (Justine) shows the line

y = 2x

the line for Velma is

y = 4x

now we need to remember that the slope (inclination) of a line is the factor of x (so, 2 and 4 in the two line equations).

a slope is expressed as y/x and indicates how many units y changes when x changes a certain amount of units (like 1).

as described (and also confirmed by the graph) the x units are minutes, and the y units are meters.

so, as per her slope, Velma moves 4 meters in 1 minute.

and Justine moves 2 meters in 1 meter.

so, Justine is half as fast as Velma.

and therefore, Justine moves a shorter distance than Velma each minute.

Answer:

Step-by-step explanation:

B and E

Answer:

hfgf td utdu6kjyyyudytdcyu6   vfhdutd,ld

Step-by-step explanation:

1. The value of A, the Net Salary received by Mr. Makatle is R 5,369.49 (R8,236,00 - R 2 866,51), which is the gross pay minus total deductions.

2. The UIF contribution of R82.36 was calculated as 1% of R8236,00 (R 8,236 x 1%).

3. Mr. Makatle's claims that the cumulative medical contributions indicated on his pay advice are incorrect are valid.

The cumulative medical contributions for the year are supposed to total R 17,640 (R 1 764,00 x 10) instead of R 6,177.00, which represents the pension's cumulative contributions.

4. Mr. Makatle's monthly tax contribution as a percentage of his gross salary is 4.8865%.

Tax contribution = R 402.45

Gross monthly salary = R 8 236

Percentage of tax contribution to gross salary = 4.8865% (R402.45/R8,236 x 100)

5. For question 2, we can use the rates computed from Mr. Makate's salary advice to calculate Danielle's net pay for the year.

Basic Salary                        FR 45 600,50

PAYE                                        R 2,228.27 (4.8865%)

UIF                                               R 456.01 (1%)

Pension Fund                        R 3 420. 04 (7.5%)

Medical Aid contribution        R 9,766.72  (21.418%)

TOTAL DEDUCTIONS           R 15,871.04

NET SALARY                       R 29,729.46

The net pay is the difference between a salary earner's gross income and the deductions made before the payment of salary.

The net pay represents the amount that the salary earner goes home with.

The net pay is also known as the take-home pay.

Mr. Paul Makatle is an employee at a clothing factory The following deductions are made from his gross monthly salary:

• 7,5% of his gross monthly salary for pension fund contributions

• UIF (Unemployment Insurance Fund) of 1% of his gross monthly salary

• PAYE (Pay as you earn) tax as per tax bracket

Use the salary advice below that Mr. Makatle receives for December 2020 to answer the questions that follow.

Basic Salary                        R 8 236,00

PAYE                                      R 402.45 (4.8865%)

UIF                                           R 82,36 (1%)

Pension Fund                        R 617,70 (7.5%)

Medical Aid contribution  R 1 764,00  (21.418%)

TOTAL DEDUCTIONS     R 2 866,51

NET SALARY                   R 5 369,49

GROSS SALARY IRP5 PARTICULARS-cumulative year to date:

R 82360,00

Total Employee's Tax R 6177.00

Medical Aid contr R 6,177.00

1. Determine the value of A, the NET salary received by Mr. Makatle

2. Show how the UIF contribution of R82.36 was calculated.

3. Mr. Makatle claims that the cumulative medical contributions indicated on his pay advice are incorrect. Verify, using calculations, whether his claim is valid

4. Calculate his monthly tax contribution as a percentage of his gross salary.

5. Calculate Danielle's net pay for the year, using Makatle's pay advice.

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Explanation:

According to the information we can infer that the change between 11 and 12 is 1.3 m/hr

To establish the value of the change in height between 11 and 12 we must look at the values of the y axis. According to this information we can establish that 11 o'clock coincides with 5.2 and 12 o'clock coincides with 3.9. So we must subtract these two values:

According to the above, we can infer that the change between these two hours is 1.3 m/hr.

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Key features for the graph given in the problem will be-:Vertex (-1, -5), Axis of symmetry=> (x = -1), y-intercept (0,-3), Minimum=> (y=-5), Domain=> (All Real), Range=>( y >= -5)

Refering to the graph given in the problem(refer image attached).The key features of the graph can be given as:

The graph has an upward-opening form, an axis of symmetry at x = -1, a y-intercept at (0, -3), a minimum point at y = -5 (which is also the vertex), and it spans all real numbers on the x-axis (domain) while being larger than or equal to -5 on the y-axis (range).

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Theoretical odds of obtaining an even number are 1/2, which equals 0.500.

The likelihood or chance of an occurrence occurring is measured by probability. It is expressed as a number between 0 and 1, where 0 denotes that the occurrence is hypothetical and 1 denotes that it is unavoidable. By dividing the number of favourable outcomes by the total number of potential outcomes, the probability of an occurrence is determined. For instance, if a coin is flipped, the likelihood that it will fall on heads is 50% because heads is the more likely of the two possible outcomes (heads or tails).

given

(a) To compute the experimental probability of getting an even number, we need to add up the number of trials in which an even number was chosen (0, 2, 4, 6, or 8) and divide by the total number of trials.

Even results are equal to 4 + 7 + 6 + 4 + 1 = 22.

There were 40 attempts in total.

In an experiment, the odds of obtaining an even number are given by the proportion of even results to all trials.

22/40 is the experimental probability of obtaining an even number.

Experimentally determined odds of receiving an even number are 0.550.

(b) Assuming the machine is fair, there are five even digits (0, 2, 4, 6, 8) and five odd digits (1, 3, 5, 7, 9), and each digit is equally likely to be chosen. Therefore, the theoretical chance of receiving an even number is 1/2.

Theoretical odds of obtaining an even number are 1/2, which equals 0.500.

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The complete question is :-   The state lottery board is examining the machine that randomly picks the lottery numbers. On each trial, the machine outputs a ball with one of the digits 0 through 9 on it. (The ball is then replaced in the machine.) The lottery board tested the machine for 40 trials and got the following results:

Answer the following. Round your answers to the nearest thousandths.

(a) From these results, compute the experimental probability of getting an even number.

(b) Assuming that the machine is fair, compute the theoretical probability of getting an even number.

0.400

(c) Assuming that the machine is fair, choose the statement below that is true.

O The experimental and theoretical probabilities must always be equal.

As the number of trials increases, we expect the experimental and theoretical probabilities to become closer, though they might not be equal.

As the number of trials increases, we expect the experimental and theoretical probabilities to become farther apart.

The value of x in ΔSTU is in the range (2, 32).

Given that ΔSTU is a triangle,

ST = 15,

US = x,

UT = 17.

We need to find the length of x in the triangle STU.

To solve this question, we need to apply the triangle inequality theorem.

According to the theorem, the sum of the lengths of any two sides of a triangle is greater than the length of the third side.

Therefore, using this theorem, we get:

ST + US > UT => 15 + x > 17

=> x > 17 - 15

=> x > 2US + UT > ST

=> x + 17 > 15 => x > 15 - 17

=> x > -2UT + ST > US

=> 17 + 15 > x

=> 32 > x

In this case ST = 15, US = x, UT = 17. Let's apply the triangle inequality to the sides of the triangle STU:

ST + US > UT

15 + x > 17

Simplify the inequality:

x > 17 - 15

x > 2

Triangle STU is valid The length of US(x) must be greater than 2 to be a perfect triangle.

However, without further information, we cannot determine the exact value of x.

You can specify any value greater than 2.

Therefore, from the above conditions, we conclude that 2 < x < 32.

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Answer:

3/4 cups

Step-by-step explanation:

3 1/2 divided by 2

Answer:

-8/15 this is the answer to you question

Answer:

d = 6

Step-by-step explanation:

10 - d = 34 - 5d

add d to both sides to make all the d's on one side

10 = 34 - 4d

subtract 34 from both sides to isolate the d and its coefficient

-24 = -4d

divide both sides by -4 to isolate d

d = 6