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3 years ago

How would the transition rule below move the figure (x,y)

Mathematics

1 answer:

exis [7]3 years ago

5 0

D. 7 units down because the y axis deals with movement up and down and since it's negative it moves down

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A man drove x miles per hour for 3 hours and (2x-60) miles per hour for the next 4.75 hours. A)Express the total distance travel

erik [133]

Answer:

$12.5x-285$ .

Step-by-step explanation:

We are told that a man drove x miles per hour for 3 hours, so he traveled 3x miles in three hours.

We are also told that he drove (2x-60) miles per hour for the next 4.75 hours. So The distance traveled by in next 4.75 hours will be:

$4.75\cdot (2x-60)=9.5x-285$

To find the total distance traveled by man we will add distances traveled by him in first 3 hours and next 4.75 hours.

$\text{The total distance traveled}=3x+9.5x-285$

Upon combining like terms we will get,

$\text{The total distance traveled}=(3+9.5)x-285$

$\text{The total distance traveled}=12.5x-285$

Therefore, the total distance traveled in terms of x will be $12.5x-285$ .

6 0

3 years ago

Of all the trees planted by a landscaping firm, 45% survive. What is the probability that 13 or more of the 15 trees they just p

Brrunno [24]

ANSWER:

The probability for 13 or more of the 15 trees they just planted will survive is 0.00110702414

SOLUTION:

Given,

The total number of plants is, n=15

The chance of survival of trees is, p=45%.

Probability of getting success p(success) = $\frac{n o \text { of favourable outcomes }}{\text {total possible outcomes}}$

P(success) = $\frac{45}{100}$

P(success) = 0.45

Binomial distribution formula is given as

$\mathrm{P}(\mathrm{X}=\mathrm{x})=\mathrm{n}_{\mathrm{C} \mathrm{x}}(\mathrm{p})^{\mathrm{x}} \cdot(1-\mathrm{p})^{\mathrm{n}-\mathrm{x}}$

In our case, x is greater than or equal to 13, i.e. x $\geq$ 13

The probability for 13 or more of the 15 trees they just planted will survive is given by

$\mathrm{P}(\mathrm{X} \geq 13)=\mathrm{P}(\mathrm{X}=13)+\mathrm{P}(\mathrm{X}=14)+\mathrm{P}(\mathrm{X}=15)$

$\mathrm{P}(\mathrm{X} \geq 13)=\left(15 \mathrm{C}_{13} \times(0.45)^{13} \times(1-0.45)^{15-13}\right.$ + $\left(^{15} \mathrm{C}_{14} \times(0.45)^{14} \times(1-0.45)^{15-14}\right.$ + $\left(15 \mathrm{C}_{15} \times(0.45)^{15} \times(1-0.45)^{15-15}\right.$

on simplification we get

$=(15 \times 7) \times(0.45)^{13} \times(0.55)^{2}+15 \times(0.45)^{14} \times(0.55)^{1}+1 \times(0.45)^{15} \times 1$

$\begin{array}{c}{=(105 \times 0.00003102863 \times 0.3025)+(15 \times 0.00001396288 \times 0.55)+} \\ {0.00000628329}\end{array}$

=0.00098554703 + 0.0001151938 + 0.00000628329

= 0.00110702414

Hence, the probability for 13 or more of the 15 trees they just planted will survive is 0.00110702414

7 0

3 years ago

A company is planning a four-year project, with an initial cost of $1.67 million. This investment cost is amortised to zero over

yaroslaw [1]

Answer:

The Net Present Value = $451180.733

Step-by-step explanation:

Given that:

the initial cost of the project is $1670000

the initial increase in working capital is $198000

The total investment will be ; initial cost of the project + initial increase in working capital

The total investment = $1670000 + $198000

The total investment = $1868000

So, This investment cost is amortised to zero over four years; This implies that the project will depreciate in four years;

Now; lets determine the rate of the annual depreciation

The annual depreciation = $\dfrac{Initial \ cost \ of \ project }{life \ of \ project}$

The annual depreciation = $\dfrac{1670000}{4}$

The annual depreciation = $417500

Over to the annual operating cash flow; the annual operating cash flow can be calculated as follows:

annual operating cash flow = (sales - cost) × (1 - tax rate )+ (annual depreciation × tax rate )

Given that the tax rate = 21% = 0.21

annual operating cash flow = (1850000 -1038000)×(1-0.21)+(417500× 0.21)

annual operating cash flow = 812000 × 0.79 + 87675

annual operating cash flow = 641480 + 87675

annual operating cash flow = $729155

So; let's calculate the after tax salvage value for the project

We know that the sales values for the project in four years is $435,000 (i.e the disposal rate of the asset after four years)

Thus; the book value is zero

The after tax salvage value for the project can now be determined by the relation:

after tax salvage value = sale value - tax (sale value - book value)

after tax salvage value = 435000 - 0.21 (435,000 -0)

after tax salvage value = 435000 - 91350

after tax salvage value = $343650

Similarly; given that the recovering rate of the project is $198000;

The cash flow in year 4 will be: annual operating cash flow + after tax salvage + recovery working capital

cash flow in year 4 = $(729155 + 343650 + 198000)

cash flow in year 4 = $ 1270805

This implies that the cash flow from year one to three is : 729155

the cash flow in year four is : 1270805

Given that the Required return rate = 16.4% = 0.164

We can therefore determine the Present cash inflows by using the relation:

$Present \ Value = \dfrac{c_1}{(1+r)^1}+ \dfrac{c_2}{(1+r)^2}+ \dfrac{c_3}{(1+r)^3}+ \dfrac{c_4}{(1+r)^4}$

$Present \ Value = \dfrac{729155}{(1+0.164)^1}+ \dfrac{729155}{(1+0.164)^2}+ \dfrac{729155}{(1+0.164)^3}+ \dfrac{1270805}{(1+0.164)^4}$

$Present \ Value = \dfrac{729155}{1.164^1}+ \dfrac{729155}{1.164^2}+ \dfrac{729155}{1.164^3}+ \dfrac{1270805}{1.164^4}$

Present Value = $(626421.8213 + 538163.0767 + 462339.413+692256.4225)

Present Value = $2319180.733

Finally, The net present value = Present Value - Total Investment

Net Present Value = $(2319180.733 - 1868000)

Net Present Value = $451180.733

Therefore; The Net Present Value = $451180.733

5 0

3 years ago

Six times the sum of a number and four

Gnoma [55]

Answer:

6*(x+4)

Step-by-step explanation:

5 0

3 years ago

Please rewrite without absolute value for the given conditions: y=|x-3|+|x+2|-|x-5|, if x <-2

alex41 [277]

Answer:

y = |x-3| + |x+2| - |x-5|, if x <-2

y = |x-3| + |x+2| - |x-5|

y = -x-3 - x+2 + x-5

y = -x -6

4 0

3 years ago