A merchant instructs his agent to buy 1,000 micro tip pens and sell them at 15% above the purchase price. the agent charges 1% commission on the purchase and 3% commission on sales and earns Rs.534/- as commission.find the price and which the agent buys the pen​

Answer:

a.) 4 half lives have passed

b) 9.388 minutes

Step-by-step explanation:

Formula for exponential growth / decay is given as:

[tex]A=A_0b^{\frac{t}{c}}[/tex]

Where [tex]A[/tex] is the final population

[tex]A_0[/tex] is the initial population

[tex]b[/tex] is the growth factor

[tex]c[/tex] is the time taken for the growth 'b'

[tex]t[/tex] is the amount of time

Here, we are given that:

[tex]A[/tex] = 6. 9 grams

[tex]A_0[/tex] = 110.4 grams

[tex]b = \dfrac{1}{2}[/tex]

[tex]c = 2.347[/tex] min

To find:

a.) Number of half lives taken for the decay.

b.) Total time in the decay.

Solution:

a.) Number of half lives taken for the decay is nothing but equal to [tex]\frac{t}{c}[/tex].

Putting the values in the formula, we get:

[tex]6.9=110.4\times \frac{1}2^{\frac{t}{c}}\\\Rightarrow 6.9=110.4\times 0.5^{\frac{t}{c}}\\\Rightarrow 0.0625=0.5^{\frac{t}{c}}\\\Rightarrow \dfrac{t}{c} =4[/tex]

Therefore, the answer is:

4 half lives have passed.

b.) Total time of decay. We have to find the value of [tex]t[/tex] here.

From answer of part a.):

[tex]\dfrac{t}{c} =4\\\Rightarrow \dfrac{t}{2.347} =4\\\Rightarrow t =\bold{9.388\ min}[/tex]

===================================================

Work Shown:

For any triangle, the three interior angles always add to 180

(4x-12) + (6x-17) + (2x+5) = 180

(4x+6x+2x) + (-12-17+5) = 180

12x - 24 = 180

12x = 180+24 ..... adding 24 to both sides

12x = 204

x = 204/12 ..... dividing both sides by 12

x = 17

We can use this x value to find the three angles

4x-12 = 4*17-12 = 56

6x-17 = 6*17-17 = 85

2x+5 = 2*17+5 = 39

As a check,

56+85+39 = 180

which confirms we have the right x value.

We see that 56 is the middle angle, so this is the second largest angle.

Answer:dusy

Step-by-step explanation:

Answer:

h = SA/(2πr) - r

Step-by-step explanation:

From what I understood of the the statement, we have to solve the equation for the variable h. So, we just have to isolate that variable in one side. See:

[tex]SA = 2\pi r^2 + 2\pi rh\\\\2\pi rh = SA - 2\pi r^2\\\\h = \dfrac{ SA - 2\pi r^2}{2\pi r}\\\\\boxed{h = \dfrac{SA}{2\pi r} - r}[/tex]

Answer:

Square root of 81 is 9

9 multiply with 4 is 36

Permiter is 36cm.

Thank you and please rate me as brainliest as it will help me to level up

Answer:

y = 3/2 ⋅  4^x

Step-by-step explanation:

I hope this helped! please mark as brainliest

Answer:

[tex]a : b = 14 : 29[/tex]

Step-by-step explanation:

Given:

[tex]Vanilla = 58[/tex]

[tex]Chocolate = 28[/tex]

Required

Represent as ratio

Let chocolate be represented with a and vanilla be represented with b

So, we have:

[tex]a : b[/tex]

[tex]a : b = 28 : 58[/tex]

Divide ratio by 2

[tex]a : b = 14 : 29[/tex]

Hence, the required ratio is [tex]14:29[/tex]

Answer:

Step-by-step explanation:

==================

Let the parts be x, y and z

As per given we get below system of equations:

Substitute 0.1x + 0.2y in the second equation:

Now we have:

and

Multiply the second equation and then subtract the first one:

Then

So the parts are:

Answer:

b

Step-by-step explanation:

Answer:

41.6

Step-by-step explanation:

32 x 0.3 = 9.6

9.6 + 32 = 41.6

41.6

i had the same question

Answer:

-2x+10

Step-by-step explanation:

f(x)=5x+8

g(x)=7x-2

(f-g)(x)= 5x+8-7x+2= -2x+10

Answer:

Only line A is a well-placed line of best fit.

Step-by-step explanation:

I did this on Plato and got it correct.

Answer:

y=1/3x-2

Step-by-step explanation:

the answer is b. the rest is so it can be enough charecters so i can post this answer

Answer:

36

Step-by-step explanation:

Number of new houses  = 60

Number of houses sold last month = (1/4) of 60

                                                          [tex]= \frac{1}{4}*60[/tex]

                                                          = 15

Remaining houses  = 60 - 15 = 45

Number of houses sold this month = (1/5) of 45

                                                          [tex]=\frac{1}{5}*45\\\\= 9[/tex]

Number of houses that are left = 45 - 9 = 36

Answer:

y = 3x + 9

Step-by-step explanation:

The perpendicular bisector to the line segment is passing through the midpoint of the line segment. Coordinates of midpoint are ( [tex]\frac{x_{1} +x_{2} }{2}[/tex] , [tex]\frac{y_{1} +y_{2} }{2}[/tex] )

Formula of slope is m = [tex]\frac{y_{2} -y_{1} }{x_{2} -x_{1} }[/tex]

Slopes of perpendicular lines are opposite reciprocals. So, if AB ⊥ CD , then [tex]m_{AB}[/tex] × [tex]m_{CD}[/tex] = - 1

y - [tex]y_{1}[/tex] = m ( x - [tex]x_{1}[/tex] )  

~~~~~~~~~~~

(- 8, 5)

(4, 1)

m = ( 5 - 1) / ( - 8 - 4) = - [tex]\frac{1}{3}[/tex]

Opposite reciprocal to ( - [tex]\frac{1}{3}[/tex] ) is 3

Coordinates of midpoint are ( - 2 , 3 )

y - 3 = 3 ( x + 2 )

y = 3x + 9  

9514 1404 393

Explanation:

The decimal equivalent of a fraction will terminate if its denominator can be factored using only the prime numbers 2 and/or 5.

1/4 = 1/(2·2) will terminate

1/15 = 1/(3·5) will not terminate

Answer:

The missing term is 10

Step-by-step explanation:

2/11=x/55

cross multiply

2*55=11x

x=10

I hope this helps :)

Answer:

The following display from a TI-84 Plus calculator presents a 99% confidence interval for a proportion.Fill in the blanks:

We are ____99%____ confident that the population mean is between ___0.385631____ and ___0.780609____.

c) 99%, 0.385631, 0.780609

Step-by-step explanation:

This is the only correct option, given the relevant population mean range.  Option B is not correct as the population mean cannot range between 0 and 0.583120 as given by the option.  Options 'a' and 'd' are not relevant to the question because they have 1% confidence level, instead of the stated 99% confidence level.

Answer:

75 hamburgers per minute

Step-by-step explanation:

We’ll it’s 4500 per hour, or every 60 minutes, to find 1 min, you can divide by 60.

4500/60 = 75

Answer:

false

Step-by-step explanation:

Answer:

The equation is [tex]y=x-9[/tex]

Step-by-step explanation:

If we want a line parallel to the line in the problem it will have the same slope. The equation given in the problem is already in slope intercept form so we can take the slope for the new equation directly from this equation.

The slope-intercept form of a linear equation is:  [tex]y=mx+b[/tex]

Where  m  is the slope and  b  is the y-intercept value.  

[tex]y=1x-2[/tex]

Therefore the slope is  

[tex]m=1[/tex]

We can now use the point-slope formula to write the equation of the parallel line:

The point-slope formula states:  

[tex](y-y1)=m(x-x1)[/tex]

Where  m  is the slope and  [tex](x1,y1)[/tex] is a point the line passes through.  

Substituting the information from the problem gives:

[tex](y- (-7)=1(x-2)[/tex]

[tex](y+7)=1(x-2)[/tex]

Or, we can solve for  y  to put the equation in slope-intercept form:

[tex]y+7=x-2[/tex]

[tex]y+7-7=x-2-7[/tex]

[tex]y+0=x-9[/tex]

[tex]y=x-9[/tex]

Answer:

$4.06 per gallon $4.06 x 7 = $28.42

Step-by-step explanation:

Answer:

[tex]\sqrt{13}[/tex]

Step-by-step explanation:

we can solve this using the distance formula: [tex]\sqrt{(x_{2}-x_1)^{2} + (y_{2}-y_1)^{2}}[/tex]

[tex]x_1, y_1[/tex] is (3, 1)

[tex]x_2, y_2[/tex] is (-1, -2)

[tex]\sqrt{(1-3)^2 + (-2-1)^2}[/tex]

which simplifies to: [tex]\sqrt{(-2)^2 + (-3)^2}[/tex]

then: [tex]\sqrt{2^2 + 3^2}[/tex] or: [tex]\sqrt{4+9}[/tex]

your final answer is: [tex]\sqrt{13}[/tex] or about 3.61

Answer:

The function is equivalent to

[tex]\frac{x+1}{x^3-x}=\frac{1}{x\left(x-1\right)}[/tex]

Step-by-step explanation:

Given the function

[tex]f\left(x\right)=\frac{x+1}{x^3-x}[/tex]

Let us simplify this function

[tex]f\left(x\right)=\frac{x+1}{x^3-x}[/tex]

        [tex]=\frac{x+1}{x\left(x+1\right)\left(x-1\right)}[/tex]     ∵ [tex]Factor\:x^3-x=x\left(x+1\right)\left(x-1\right)[/tex]

Cancel the common factor (x+1)

        [tex]=\frac{1}{x\left(x-1\right)}[/tex]

Therefore, the function is equivalent to

[tex]\frac{x+1}{x^3-x}=\frac{1}{x\left(x-1\right)}[/tex]

Answer:

wrong

Step-by-step explanation:

Answer:

1) x = 1  ,  y = 2

2) x=3, y=-2

3) x=3, y=-4

4) x=0, y=-3

Step-by-step explanation:

I hope this helped! please mark as brailiest

Answer:

0.5

Step-by-step explanation:

The answer of this problem would be 5.5, so you are missing the 0.5

Answer :

1/2

Explanation :

Completed the assignment on Edge.