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1 year ago

If 2^2008 – 2^2007 - 2^2006 + 2^2005 = k * 2^2005 then the value of k is equal to

Mathematics

2 answers:

Tanzania [10]1 year ago

8 0

Answer:

k = 3

Step-by-step explanation:

$2^{2008}-2^{2007}-2^{2006}+2^{2005}=k \times 2^{2005}$

$=> (2^{2005} \times 2^3) - (2^{2005} \times 2^2) - (2^{2005} \times 2^1) + 2^{2005} = k \times 2^{2005}$

Take $2^{2005}$ common from all the terms in L.H.S.

$=> 2^{2005}(2^3 - 2^2 - 2^1 + 1) = k \times 2^{2005}$

Divide both the sides by $2^{2005}$ .

$=> \frac{2^{2005}(2^3 - 2^2 - 2^1 + 1)}{2^{2005}} = \frac{k \times 2^{2005}}{2^{2005}}$

$=> 2^3 - 2^2 - 2^1 + 1 = k$

Expand the terms in L.H.S.

$=> 8 - 4 - 2 + 1 = k$

$=> k = 3$

scZoUnD [109]1 year ago

5 0

Step-by-step explanation:

Maths

Bookmark

if 2

2008

−2

2007

−2

2006

2005

=k ⋅2

2005

then the value of k is equal to

Answer

Correct option is

2008

−2

2007

−2

2006

2005

=k⋅2

2005

⇒[2

2008

−2

2006

]−[2

2007

−2

2005

]=k⋅2

2005

⇒2

2006

−1)−2

2005

−1)=k⋅2

2005

⇒3(2

2006

−2

2005

)=k⋅2

2005

⇒3[2

2005

(2−1)]=k⋅2

2005

⇒3(2

2005

)=k⋅2

2005

On comparing, we get

k=3

Hence, Option B is correct.

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A store receives shipments of peaches and wants to sort them by weight. Drag each shipment to match the ratio of peaches to poun

Andrej [43]

Answer:

Step-by-step explanation:

Given that a store receives shipments of peaches. They want to sort them by weight.

The sorting pattern is as follows:

Peaches : Pound = 2:1 or 3.25:1 or 1:3.25

Given are i) 26 peaches to 13 lbs = 26:13=2:1 Hence goes to the first box

ii) 6 peaches to 19.5 lbs =6:19,5 = 1:3,25 lb. Hence goes to II box

iii) 13 peaches to 4 lbs: =13:4=3.25:1 Hence goes to II box

iv) 39 peaches to 12 lbs: =39:12=3.25:1 Hence goes to II box

v) 15 peaches to 7.5 lbs: =15:7.5=2:1 Hence goes to I box

i - I box

ii - II box

iii - II box

iv) - II box

v) - I box

8 0

2 years ago

The unit cost, in dollars, to produce bins of cat food is $3 and the fixed cost is $6972. The price-demand function, in dollars

stellarik [79]

Answer:

Revenue , Cost and Profit Function

Step-by-step explanation:

Here we are given the Price/Demand Function as

P(x) = 253-2x

which means when the demand of Cat food is x units , the price will be fixed as 253-2x per unit.

Now let us revenue generated from this demand i.e. x units

Revenue = Demand * Price per unit

R(x) = x * (253-2x)

= $253x-2x^2$

Now let us Evaluate the Cost Function

Cost = Variable cost + Fixed Cost

Variable cost = cost per unit * number of units

= 3*x

= 3x

Fixed Cost = 6972 as given in the problem.

Hence

Cost Function C(x) = 3x+6972

Let us now find the Profit Function

Profit = Revenue - Cost

P(x) = R(x) - C(x)

= $253x-2x^2 - (3x + 6972)$

= $253x-3x-2x^2-6972\\= 250x-2x^2-6972\\=-2x^2+250x-6972\\$

Now we have to find the quantity at which we attain break even point.

We know that at break even point

Profit = 0

Hence P(x) = 0

$-2x^2+250x-6972=0\\$

now we have to solve the above equation for x

Dividing both sides by -2 we get

$x^2-125x+3486=0$

Now we have to find the factors of 3486 whose sum is 125. Which comes out to be 42 and 83

Hence we now solve the above quadratic equation using splitting the middle term method .

Hence

$x^2-42x-83x+3486=0\\x(x-42)-83(x-42)=0\\(x-42)(x-83)=0\\$

Either (x-42) = 0 or (x-83) = 0 therefore

if x-42= 0 ; x=42

if x-83=0 ; x=83

Smallest of which is 42. Hence the number of units at which it attains the break even point is 42.

5 0

2 years ago

If the egress rate for a stadium is 5,500 fans per hour and it takes fans about one-third less time for fans to exit a game as i

Marina CMI [18]

Answer:

1833 fans per hour

Step-by-step explanation:

Ingress is entering and Egress is exiting.

Since exiting time is 1/3rd less than entering time, we have 5500 people exiting, so ingessing would be 1/3rd that.

Thus,

Ingress Rate = 5500/3 = 1833.33

Rounding to whole number, we have 1833 fans per hour

4 0

2 years ago

Read 2 more answers

If ray NP bisects <MNQ, m<MNQ=(8x+12)°, m<PNQ=78°, and m<RNM=(3y-9)°, find the value of x and y

aksik [14]

Step 1

Find the measure of angle x

we know that

If ray NP bisects <MNQ

then

m<MNQ=m<PNM+m<PNQ ------> equation A

and

m<PNM=m<PNQ -------> equation B

we have that

m<MNQ=(8x+12)°

m<PNQ=78°

substitute in equation A

(8x+12)=78+78-------> 8x+12=156------> 8x=156-12

8x=144------> x=18°

Step 2

Find the measure of angle y

we have

m<PNM=(3y-9)°

m<PNM=78°

3y-9=78------> 3y=87------> y=29°

therefore

the answer is

the measure of x is 18° and the measure of y is 29°

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2 years ago

How is the graph of y = negative RootIndex 3 StartRoot x minus 4 EndRoot transformed to produce the graph of y = negative RootIn

SVEN [57.7K]

Answer:

Multiply by ∛2 and translate the graph to left by 4 units.

Step-by-step explanation:

The initial function given is:

y = -∛(x - 4)

The transformed function is:

y = -∛(2x - 4)

Consider the initial function.

y = -∛(x - 4)

(Represented by Black line in the graph)

Multiply the function by ∛2. The function becomes:

y = -∛(x - 4) × ∛2

y = -∛(2)(x-4)

y = -∛(2x-8)

(Represented by Red line in the graph represents this function)

Translate the graph 4 units to the left by adding 4 to the x component:

y = -∛(2x-8+4)

y= -∛(2x - 4)

(Represented by Blue line in the graph)

3 0

2 years ago

Read 2 more answers

If 2^2008 – 2^2007 - 2^2006 + 2^2005 = k * 2^2005 then the value of k is equal to​

If 2^2008 – 2^2007 - 2^2006 + 2^2005 = k * 2^2005 then the value of k is equal to