In 2014 , a salesman was paid a basic monthly salary of rs 25 000. At the end of the year ,he was also paid a bonus of 6.5 % of the value of the sales that he had made during the year . his sales for the year was rs 100 000. calculate his totasl income that he receives in 2014.

The rate of current in the stream on that​ day is; 2 miles per hour

When dealing with relative velocity, we can say that;

When the motorboat travels downstream, then it means the total velocity will be;

Total velocity = Velocity of the motorboat in still water + Velocity of the stream.

If the motorboat travels upstream, the total velocity will be;

Total velocity = Velocity of the motorboat in still water - Velocity of the stream.

Thus,

Upstream speed = (14 mi/h - S)

Downstream speed = (14 mi/h + S)

Where;

S is the rate of current in the stream.

We are told that going downstream, it takes 15 minutes more to travel 12 miles, then we can write the system of equations as;

(14 mi/h + S)*T = 12 mi

(14 mi/h - S)*(T - 15 min) = 12 mi

Making T the subject in the first equation gives;

T = (12 mi)/(14 mi/h + S)

Plugging in (12 mi)/(14 mi/h + S) for T in the second equation gives;

(14 mi/h - S)*((12 mi)/(14 mi/h + S) - 15 min) = 12 mi

Multiply both sides by (14 mi/h + S) to get;

(14 mi/h - S)*12 mi  - (14 mi/h + S)*(14 mi/h - S)*(- 15 min) = 12 mi*(14 mi/h + S)

Since the speeds are in miles per hours, we can rewrite as:

- 15 min = -0.25 h

(14 mi/h - S)*12 mi  - (14 mi/h + S)*(14 mi/h - S)*(- 0.25 h) = 12 mi*(14 mi/h + S)

168 mi²/h - 12mi*S  + 49mi²/h + 0.25h*S² = 168mi²/h + 12mi*S

- 12mi*S  + 49mi²/h - 0.25h*S² = 12mi*S

-24mi*S -  0.25h*S²  + 49mi²/h = 0

Solving this quadratic equation with online quadratic equation solver gives us; S = 2 mph

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Answer:

x( x-4)(x+2)

Step-by-step explanation:

x^3-2x^2-8x

First factor out the greatest common factor x

x( x^2 -2x -8)

What 2 numbers multiply to -8 and add to -2

-4*2 = -8

-4+2 = -2

x( x-4)(x+2)

Answer:

Your answer is -13x + 20

Step-by-step explanation:

2x - 5*(3x - 4)

Discribute the -5.

2x + [ (-5)(3x) + (-5)(-4) ]

2x + [ (-15x +20) ]

2x - 15x + 20

- 13x + 20

The rate of interest  for the given data can be found as 6%.

Simple interest can be defined as a form of interest in which the percent rate is applied on the same principal for a given period of time. The amount can be calculated by adding the interest to the principal.

The given data as per the question is as below,

P = $4000, t = 6 years and Interest = $1440.

Suppose the rate of interest be r% per annum.

Substitute all the values in the expression for simple interest (P × r × t)/100 as follows,

1440 = (4000 × 6 × r)/100

⇒ r = 6%

Hence, the rate of interest is obtained as 6%.

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Answer:

2x-2y-3z

Step-by-step explanation:

8x+-6x

=8x-6x

=2x

-9y+7y

=-2y

2z+-5z

= 2z-5z

=-3z

2x-2y-3z

8x - 9y + 2z

-6x + 7y - 5z

On adding these two equation :

8x + ( -6x) = 2x

-9y + 7y = -2y

2z + (-5z) = -3z

we will get :

2x - 2y -3z

.

In the addition/subtraction method, the two equations in the system are added or subtracted to create a new equation with only one variable. In order for the new equation to have only one variable, the other variable must cancel out. In other words, we must first perform operations on each equation until one term has an equal and opposite coefficient as the corresponding term in the other equation.

.

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Answer:

3

Step-by-step explanation:

His total doubles 73 and he already has 13 doubles. So, 73-13 = 60.He needs 60 doubles. His current age is 12. So, 17-12 = 5 yrs. 1 yr has 4 season. For 5 yrs 20 season. 60/20 = 3. Hence 3 doubles/season

by sethus1981.

Answer:

4

Step-by-step explanation:

gradient = slope = m = rise / run

  from the origin (0,0) this line rises '12' and has a run of '3'

             12/3 = 4

Answer:

{ No SIMPLIFIED: [tex]\frac{9}{12} inches[/tex] }
{ SIMPLIFIED: [tex]\frac{3}{4} inches[/tex] }

Step-by-step explanation:

If we want to know about the plant grows, we need to add the fractions in 3 weeks with this solution:
[ The inch of the plant 1st week ] + [ The inch of the plant 2nd week ] + [ The inch of the plant 3rd week ] = [ The inch of the plant in 3 weeks ]

Look at the denominator of 3 weeks, it is 12 and the numerators are 1,3,5
To plus the fraction we remain the denominator and plus the numerators together which we can result in this equation:
[tex]\frac{1}{12}[/tex] + [tex]\frac{3}{12}[/tex] + [tex]\frac{5}{12}[/tex] = [tex]\frac{1 + 3 + 5}{12}[/tex] = [tex]\frac{9}{12}[/tex] { SIMPLIFIED: [tex]\frac{9 : 3 }{12 : 3} = \frac{3}{4}[/tex] }
So then we see that if you choose no simplified then: Michael's plant grow  [tex]\frac{9}{12}[/tex] inches in 3 weeks or you could choose the simpliflied one then: Michael's plant grow [tex]\frac{3}{4}[/tex] inches in 3 weeks.

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We can begin by rewriting the problem:

3/4 - 1/2p > 5/4

Let’s solve accordingly through steps:

1. Subtract 3/4

-1/2p > 2/4

2. Divide both sides by the coefficient

-1/2 / -1/2 = p

2/4 / -1/2 = -1

3. Simplify & Switch Signs

p < -1

The answer to Part A is p < -1.

Part B: On a number line, this answer would be graphed by plotting a point at -1 and drawing an arrow that goes to the left direction to show that p is less than -1.

Answer:

sorry I don't know now how to read

Answer:

y = 4x - 2

Step-by-step explanation:

y = 4x + b

-6 = 4(-1) + b

-6 = -4 + b

b = -2

y = 4x - 2

Answer:

[tex]y - (-6) = 4(x - (-1))[/tex] or [tex]y = 4x - 2[/tex]

Step-by-step explanation:

We can use point slope form: [tex]y - y_{1} = m(x - x_{1})[/tex], where [tex](x_1, y_1)[/tex] is a point on the line and [tex]m[/tex] is the slope.

We plug in (-1, -6) and 4 to get:  which simplifies to [tex]y + 6 = 4(x + 1)[/tex]

If we want to express this in the form y = mx + b, we have to do a little rearranging. [tex]y + 6 = 4(x + 1)[/tex] becomes [tex]y + 6 = 4x + 4[/tex] and then we subtract 6 from both sides to get: [tex]y = 4x - 2[/tex]

The two sequence A and sequence B both are correct.

Graph is a mathematical representation of a network and it describes the relationship between lines and points.

Given that triangle UVW and Triangle ABC are congruent.

A transformation is a way of changing the size or position of a shape.

Every point in the image is the same distance from the mirror line as the original shape.

Triangle UVW made a 180 degrees of rotation about point V and then a triangle along the directed line segment VB.

This is same as translation along the directed line segment UA then about 180 degrees rotation about point A.

Hence, the two sequence A and sequence B both are correct.

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The Least Common Multiplier of [tex]$q(2-4), r(-6-8), s(-102), t(-26)$[/tex] is [tex]$-9282 q r s t$[/tex].

What is Least Common Multiplier ?

The smallest positive integer that is divisible by both a and b is known as the least common multiple (lcm), lowest common multiple (lcm), or smallest common multiple of two numbers a and b in mathematics and number theory.

Lowest Common Multiplier (LCM)

The LCM of a, b is the smallest multiplier that is divisible by both a and b

Factor [tex]$q(2-4): \quad-2 q$[/tex]

Factor [tex]$r(-6-8): \quad-2 \cdot 7 r$[/tex]

Factor [tex]$s(-102): \quad-17 \cdot 2 \cdot 3 s$[/tex]

Factor [tex]$t(-26): \quad-13 \cdot 2 t$[/tex]

Multiply each factor with the highest power:

[tex]$$-13 \cdot 17 \cdot 2 \cdot 3 \cdot 7 \cdot q \cdot r \cdot s \cdot t$$[/tex]

Simplify

[tex]$-9282 q r s t$[/tex]

Complete question: Find the Least Common Multiplier  of Q(2, -4), R(-6, -8), S(-10, 2), T(-2, 6) is:

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The function that models the data in the given table is: D. y = -2x + 10.

The function that models the data of a table can be expressed in the slope-intercept form as y = mx + b, where:

Find the slope of the function using two pairs of values from the table, (6, -2) and (10, -10):

Slope (m) = change in y / change in x = (-10 - (-2)) / (10 - 6)

Slope (m) = -8 / 4

Slope (m) = -2

Find the y-intercept (b) by substituting m = -2 and (x, y) = (6, -2) into y = mx + b:

-2 = -2(6) + b

-2 = -12 + b

-2 + 12 = b

10 = b

b = 10

To write the function, substitute m = -2 and b = 10 into y = mx + b:

y = -2x + 10

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Kenji and Ramon are at a distance of 750 m after a time interval of 1 hour from each other.

Kenji runs for a total time of 60 minutes + 15 minutes = 75 minutes.

Ramon runs for a total of 60 minutes.

Now, we find the total distance covered by Kenji and Ramon in the time intervals of 75 minutes and 60 minutes respectively.

Kenji runs a total distance of 150 meters/minute * 75 minutes = 11250 meters.

Ramon runs a total distance of 200 meters/minute * 60 minutes = 12000 meters.

Now, we find the difference in their distances.

The distance between Kenji and Ramon is 12000 meters - 11250 meters = 750 meters.

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Complete Question:

Kenji and Ramon are running cross country. Kenji run at a rate of 150 meter per minute and Ramon runs at a rate of 200 meters per minute. If Kenji starts 15 minutes before Ramon, how far apart are they after one hour?

This confidence interval suggests that we are 90% confident that the population mean lies between $273 and $658.

This confidence interval provides us with an estimate of the population mean with 90% confidence. This confidence interval suggests that we are 90% confident that the population mean lies between $273 and In other words, we can be 90% sure that the population mean falls within this range. This confidence interval does not tell us the actual population mean, but it provides us with an estimate of where the population mean is likely to lie. Furthermore, it also provides us with an indication of the degree of uncertainty associated with our estimate.

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Two triangles are similar when their corresponding angles are congruent, and the corresponding sides are proportional. Hence, option C s the most appropriate answer to the given question.

When we are given triangles, we can prove that two triangles are similar to the given conditions by applying various tests of similarity.

Similar triangles are triangles that have the same shape, but they may have different sizes.

Hence, to prove them to be similar, we have to prove the corresponding angles are congruent and the corresponding sides are proportional. Hence, option C is the only right choice for the given question.

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The line integral of the vector field in the figure is zero. This is due to the fact that the vector field is perpendicular to the curve c, and therefore, the integral of the dot product of the vector field and the tangent vector along the curve c is zero.

1. The line integral of a vector field is the integral of the dot product of the vector field and the tangent vector of the curve along the curve.

2. The vector field in the figure is perpendicular to the curve c.

3. The dot product of two perpendicular vectors is zero.

4. Therefore, the integral of the dot product of the vector field and the tangent vector along the curve c is zero.

5. Hence, the line integral of the vector field in the figure is zero.

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the impact on the error probability of part is on  Decreasing trends of the test procedure

A Type II error is when we fail to reject a false null hypothesis. Higher values of α make it easier to reject the null hypothesis, so choosing higher values for α can reduce the probability of a Type II error.

The consequence here is that if the null hypothesis is true, increasing α makes it more likely that we commit a Type I error (rejecting a true null hypothesis).

So using lower values of α can increase the probability of a Type II error.

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The value of the double integral ∫∫3x sin(x + y) dA, R = [0, π/6] × [0, π/3] is  0.677

In this question we need to calculate the double integral. 3x sin(x + y) dA, R = [0, π/6] × [0, π/3]

i.e., to find ∫∫3x sin(x + y) dA, R = [0, π/6] × [0, π/3]

First we integrate the function 3x sin(x+y) as a function of y, treating the variable x as a constant.

G(x) = ∫_[0, π/6] (3x sin(x+y)) dy

G(x) = 0.402 xcos(x) + (3x sin(x) / 2)

Now we calculate the integral of the previous result as a function of x.

i.e., ∫_[0, π/3] G(x) dx

= ∫_[0, π/3] [0.402 xcos(x) + (3x sin(x) / 2)] dx

= 0.677

Therefore, the solution to the double integral. 3x sin(x + y) da, r = [0, π/6] × [0, π/3] is  0.677

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Fred's pay for the specified week, with a rate of $11.25 for regular hours and time and a half for overtime, and number of hours worked of 48.5 hours is presented by completing the attached table as follows;

Rate: $11.25, regular hours: 40, overtime: N/A, total: $450

Rate: $16.875, regular hours: N/A, overtime: 8.5, total: $143.4375

Gross: $593.4375

A payment rate is the amount of payment or money that is received in a unit of time.

The amount Fred earns per hour = $11.25

The number of regular hours Fred works per week = 40

The rate at which he is paid for overtime = Time and a half

The number of hours Fred works in the specified week = 48.5 hours

Therefore, the amount Fred earns for working overtime = 1.5 × $11.25 = $16.875

The amount Fred earns for regular hours during the specified week = 40 × $11.25 = $450

The number of overtime hours Fred works for during the week = 48.5 - 40 = 8.5

The amount Fred earns for the overtime work = 8.5 × $16.875 = $143.4375

Fred's gross payment for the week is therefore; $450 + $143.4375 = $593.4375

The table can therefore be completed by plugging in the above values as follows;

Rate: $11.25, regular hours: 40, overtime: N/A, total: $450

Rate: $16.875, regular hours: N/A, overtime: 8.5, total: $143.4375

Gross: $593.4375

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Answer:

Step-by-step explanation: To find the measure of angle ACB, we can use the Pythagorean Theorem: AB^2 + AC^2 = BC^2.

Substituting in the given values for AB and AC, we get: 10.2^2 + 4.9^2 = BC^2

Solving for BC, we get: BC = √(10.2^2 + 4.9^2)

Substituting this value back into the equation for the Pythagorean Theorem, we get:

AB^2 + AC^2 = (√(10.2^2 + 4.9^2))^2

Simplifying this equation, we get:

AB^2 + AC^2 = 10.2^2 + 4.9^2

This equation is already in the correct form, so we can solve for ∠ACB directly:

∠ACB = tan^-1(AC/AB)

Substituting in the given values for AC and AB, we get:

∠ACB = tan^-1(4.9/10.2)

Using a calculator, we find that tan^-1(4.9/10.2) is approximately equal to 26.7°.

Rounded to 3 significant figures, this value is 26.7°.

Answer:

The slope of the line is = 3/2

Answer:

Equation in Point Slope Form: y= 3/2x - 3

Step-by-step explanation:

Point slope form is y=mx+b

where m is the slope of the line (rise over run) which in this case is 3/2

b is the y intercept (where the line crosses the y axis) which in this case is at point (0,-3)

The [tex]\vec{v}[/tex] as an ordered triplet of values, separated by commas is ( 0 , 0 , 10 )

The magnitude of V is 10 units.

The sine of the angle between  [tex]\vec{T}[/tex] and [tex]\vec{U}[/tex] is [tex]45^{\circ}[/tex].

As per the given data the value of [tex]\vec{T}[/tex] is ( 3, 1, 0 ) and [tex]\vec{U}[/tex] is ( 2, 4, 0 )

Firstly we have to determine the value of [tex]\vec{v}[/tex].

The value of [tex]\vec{v}[/tex] is given by [tex]\vec T \times \vec U[/tex]

[tex]& v=\left|\begin{array}{lll}\hat{i} & j & \hat{k} \\3 & 1 & 0\\2 & 4 & 0\end{array}\right|[/tex]

[tex]=\hat{k}(12-2)[/tex]

[tex]=10 \hat{k}[/tex]

Therefore [tex]\vec{v}[/tex] = ( 0 , 0 , 10 )

Now we have to determine the value of magnitude of V.

Magnitude of V is represented by [tex]$|\vec{v}|[/tex]

[tex]$|\vec{v}|=\sqrt{100}[/tex]

[tex]$|\vec{v}|[/tex] = 10 units

Therefore the magnitude of V is 10 units.

Now we have to determine the value of sine of the angle between  [tex]\vec{T}[/tex] and [tex]\vec{U}[/tex].

[tex]|\vec{v}|=|\tilde{T}||\tilde{U}| \sin \theta_{T U}[/tex]

[tex]\Rightarrow \theta_{T U}=\sin ^{-1}\left(\frac{|\vec{v}|}{|\vec{T}| |\vec{U}|}\right)[/tex]

[tex]=\sin ^{-1}\left(\frac{10}{\sqrt{200}}\right)[/tex]

[tex]=45^{\circ}[/tex]

Therefore value of sine of the angle between  [tex]\vec{T}[/tex] and [tex]\vec{U}[/tex] is [tex]45^{\circ}[/tex]

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The graph is a parabola with its touching the x-axis at (3,0)

A parabola is a curve where any point is at an equal distance from:

a fixed point (the focus ), and

a fixed straight line (the directrix )

its general equation is y = a(x – h)² + k or x = a(y – k)² +h. Here (h, k) denotes the vertex. y = a(x – h)2 + k is the regular form. x = a(y – k)2 +h is the sidewise form.

Given here (x-3)² + 4 = -4/9(x(x-6))

simplifying this we get

9(x²-6x+13) = -4 (x(x-6))

13x²-78x+117 = 0

(x-3)² = 0

thus it has a root at x=3

The graph is attached showing the parabola  touching the x-axis at (3,0)

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Answer:

x = 13

Step-by-step explanation:

vertical angles are congruent , then

∠ B = ∠ A , that is

6x - 8 = 5x + 5 ( subtract 5x from both sides )

x - 8 = 5 ( add 8 to both sides )

x = 13

Answer:

3.75 Hours or 225 Minutes

Step-by-step explanation:

5/4 = 1.25 So it takes 1.25 hours to do an assignment

1.25 x 3 = 3.75

Which equals 225 Minutes

Answer: 3.75 or 3 3/4

Step-by-step explanation:

This is a unit rate problem

A unit rate is a rate for one of something. (i.e, 1 pencil for 4 notebooks)

So first, to find the time needed for one assignment, we divided 5 hours by 4 hours.

5/4 = 1.25 (1 and 1/4)

Now we multiply the unit rate by 3.

1.25 times 3 = 3.75, or 3 3/4.

M will increase from 24 to 56

The relationship between two values where their ratio equals a constant number is known as a direct proportion or direct variation. It is symbolised by the proportional sign ().

According to the direct proportion formula, if y is directly proportional to x, we can state that y = kx, where k is a constant. Y = kx also serves as the direct proportion equation's general form.

When one quantity increases or declines, the other quantity also rises or falls in direct proportion. On the other hand, in indirect or inverse proportion, if one quantity rises, the other one falls, and vice versa.

m= 8p

When p = 3        

 m =3 × 8 =24

When p = 47      

  m=8× 7 = 56

So M will increase from 24 to 56

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The rate of change of S for the weekly sales is :

-250 000e⁻°·⁵t

Given:

the sales of the product is :

S = 500,000e^-0.5t

where S is the weekly sales in the dollars and t is the number of weeks since end of the campaign.

we are asked to find the rate of sales dS/dt = ?

that is the rate of sales of delay.

Given:

S = 500,000e^-0.5t

dS/dt =(500,000)e^-0.5t + 500,00 (e^-0.5t)

= 0 +  500,00 (e^-0.5t)

= - 250 000 e^0.5t

therefore, dS/dt = - 250 000 e^0.5t

Hence we get the required answer.

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For the scientific method , the true statement about the hypothesis is  (b) research studies are designed to prove a hypothesis.

The term Hypothesis is defined as the observation which is proposed as the possible outcome or results of an experiment .

we know that ; in order to prove a hypothesis, the experiments are designed and after that they are performed based on given hypothesis.

That is how the experiments are designed based on a previous idea which may result in a particular outcome.

So , any hypothesis is dependent on a specific experiment( research studies) .

Therefore , the correct option is (b) .

The given question is incomplete , the complete question is

In the scientific method, which of the following is true about a hypothesis?

(a) the same hypothesis may not be tested more than once.

(b) research studies are designed to prove a hypothesis.

(c) a specific hypothesis is generated based on an established theory.

(d) a hypothesis both explains and predicts a phenomenon.

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