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iVinArrow [24]
4 years ago
14

Determine whether the dilation from Figure A to Figure B is a reduction or an enlargement

Mathematics
1 answer:
katrin [286]4 years ago
5 0

Answer:

see explanation

Step-by-step explanation:

Since figure B is smaller than Figure A then Figure B is a reduction.

To find the scale factor, calculate the ratio of corresponding sides, image to original.

Using the base lines of both triangles, then

scale factor k = \frac{2}{6} = \frac{1}{3}

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6. A submarine has three navigational devices but can remain at sea if at least two are working. Suppose that the failure times
horsena [70]

Answer:

The three survival functions are e-t, e-2/3t and e-1/3t

Then, the rate of the second death equals (multiplying all combinations of 1 survival + 1 death * the rate of death of the third device)

(e-t*(1-e-2/3t)+(1-e-t)e-2/3t)1/3e-1/3t +

(e-t*(1-e-1/3t)+(1-e-t)e-1/3t)2/3e-2/3t  +

(e-2/3t*(1-e-1/3t)+(1-e-2/3t)e-1/3t)e-t =

1/3e-4/3t + 1/3e-t -2/3e -2t +

2/3e -5/3t + 2/3e-t -4/3e -2t +

e -4/3 + e -5/3 -2e -2t =

e-t + 4/3e-4/3t + 5/3e-5/3t - 4e-2t

Note that this integrates to 1, thus satisfying one of the rules of a density. We also can see that this function is greater than 0, as e-t + 4/3e-4/3t + 5/3e-5/3t - 4e-2t =

e-t + 4/3e-4/3t + 5/3e-5/3t - e-2t - 4/3e-2t - 5/3e-2t =

e-t  - e-2t + 4/3e-4/3t - 4/3e-2t + 5/3e-5/3t- 5/3e-2t =

e-t (1 - e-t) + 4/3e-4/3t(1 - e-2/3t) + 5/3e-5/3t(1 - e-1/3t) > 0 for t > 0

Then, to find the average length that the ship is at sea, we must integrate

t(e-t + 4/3e-4/3t + 5/3e-5/3t - 4e-2t) from 0 to infinity.

However, as a shortcut, note that we can easily identify the integral of the first three functions,

te-t, 4/3te-4/3t, and 5/3te-5/3t, as calculating the expected value of the exponential distribution with parameters 1, 4/3, and 5/3, and the expected value is 1, 3/4, and 3/5

For the final function, 4te-2t = 2*2e-2t , this is twice the expected value of the exponential distribution with parameter 2 = 2 * 1/2 = 1

1 + 3/4 + 3/5 - 1 = 27/20

Step-by-step explanation:

5 0
4 years ago
The value of a new car decreases by about 15% in the first year. How much will a car be worth after one year if its initial valu
Masja [62]

Answer:

(a)

$850.

(b)

$4250.

(c)

$4267.

Step-by-step explanation:

It is given that the value of a new car decreases by about 15% in the first year.

(a)

Now we are asked to find the cost of a car after one year; if we are given the initial value of car=$1000.

As the rate decreases by 15%.

that means we have to pay (100-15)% of the initial amount.

i.e. we have to pay 85% of the initial amount.

Hence the amount one has to pay= 85% of 1000.

which is equal to =85%×1000

⇒   =\dfrac{85}{100}\times 1000\\\\=85\times 10\\\\=850

Hence, the amount of car after one year when initaial amount is $1000 is:

$850.

(b)

if initial amount=$ 5000

then amount one has to pay after one year:

85\%\times 5000\\ \\=\dfrac{85}{100}\times 5000\\\\=4250

Hence, the amount of car after one year when initaial amount is $5000 is:

$4250.

(c)

if initial amount=$ 5020

then amount one has to pay after one year:

85\%\times 5020\\ \\=\dfrac{85}{100}\times 5020\\\\=4267

Hence, the amount of car after one year when initaial amount is $5020 is:

$4267.

7 0
3 years ago
Suppose the only measuring cup you own is a one-third measuring cup. Using this measuring cup how many scoops will you need to h
Mariulka [41]

Answer:

11

Step-by-step explanation:

for each full cup of sugar, you need 3 one-third measuring cups.

we have 3 full cups so 3×3=9

and another 2 for the 2/3, 9+2=11

so a total of 11 scoops

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2 years ago
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3 years ago
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