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vovikov84 [41]
3 years ago
15

Find the least mean square estimate ofxbased on the observationy=y.

Mathematics
1 answer:
bija089 [108]3 years ago
7 0
Ndenkdendekwnndnndnd
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What conclusions can be made about the amount of money in each account if f represents Molly's account and g represents her brot
Nat2105 [25]

Answer:

(b) is true

Step-by-step explanation:

Given

Molly

a = 500 --- starting balance

m = 10 --- monthly rate

Her brother

a = 100 ---- starting balance

r = 10\% --- annual rate

Required

Determine which option is true

First, we calculate her brother's function.

The function is an exponential function calculated as:

y = ab^x

Where b = 1 + r

So, we have:

y = ab^x

y = 100 *(1 + 10\%) ^x

y = 100 *(1 + 0.10) ^x

y = 100 *(1.10) ^x

Hence:

g(x) = 100 *(1.10) ^x

Next, we calculate Molly's function (a linear function)

The monthly function is:

y = mx + a

So, we have:

y = 10x + 500

Annually, the function will be:

y = 10x*12 + 500

y = 120x + 500

So, we have:

f(x) = 120x + 500

At this point, we have:

f(x) = 120x + 500 ---- Molly

g(x) = 100 *(1.10) ^x ---- Her brother

<u>Next, we test each option</u>

(a): Molly's account will have a faster rate of change over [32,40]

We calculated Molly's function to be:

y = 120x + 500

The slope of a linear function with the form: y = mx + b is m

By comparison:

m = 120

Since Molly's account is a linear function, the rate of change over any interval will always be the same; i.e.

m = 120

For his brother:

Rate of change is calculated using:

m = \frac{g(b) - g(a)}{b - a}

m = \frac{g(40) - g(32)}{40 - 32}

m = \frac{g(40) - g(32)}{8}

Calculate g(40) and g(32)

g(x) = 100 *(1.10) ^x

g(40) = 100 * 1.10^{40} =4526

g(32) = 100 * 1.10^{32} = 2111

So, we have:

m = \frac{4526 - 2111}{8}

m = \frac{2415}{8}

m = 302

By comparison: 302 > 120

Hence, her brother's account has a faster rate over [32,40]

(a) is false

(b): Molly's account will have a slower rate of change over [24,30]

m = 120 --- Molly's rate of change

For his brother:

m = \frac{g(b) - g(a)}{b - a}

m = \frac{g(30) - g(24)}{30 - 24}

m = \frac{g(30) - g(24)}{6}

Calculate g(30) and g(24)

g(x) = 100 *(1.10) ^x

g(40) = 100 * 1.10^{30} =1745

g(32) = 100 * 1.10^{24} = 985

So, we have:

m = \frac{g(30) - g(24)}{6}

m = \frac{1745 - 985}{6}

m = \frac{760}{6}

m = 127

By comparison: 127 > 120

Hence, Molly's account has a slower rate over [24,30]

(b) is false

(c): Molly's account will have a slower rate of change over [0,4]

m = 120 --- Molly's rate of change

For his brother:

m = \frac{g(b) - g(a)}{b - a}

m = \frac{g(4) - g(0)}{4 - 0}

m = \frac{g(4) - g(0)}{4}

Calculate g(4) and g(0)

g(x) = 100 *(1.10) ^x

g(4) = 100 * 1.10^4 =146

g(0) = 100 * 1.10^{0} = 100

So, we have:

m = \frac{g(4) - g(0)}{4}

m = \frac{146 - 100}{4}

m = \frac{46}{4}

m = 11.5

By comparison: 120>11.5

Hence, Molly's account has a faster rate over [0,4]

(c) is false

4 0
3 years ago
I really need help on this one!!
faltersainse [42]
137 because it’s the same as the angle given.
8 0
3 years ago
Read 2 more answers
The utility industry had 428.5 thousand jobs in 2010 and is expected to decline at an average rate of 3 thousand jobs per year f
e-lub [12.9K]

Answer:

Utility's percent Change from 2010 to 2020 = 7%

Step-by-step explanation:

Jobs available at the utility industry in 2010= 428.5 thousand

Average rate of decline = 3 thousand

Years between 2010 and 2020

Utility's percent Change from 2010 to 2020 = Total change in jobs / jobs in 2010 × 100

Total change in jobs:

There are 10 years between 2010 and 2020

Jobs decline at an average of 3 thousand per year

Total change in jobs= 10 years × 3 thousand

= 30 thousand

Utility's percent Change from 2010 to 2020 = Total change in jobs / jobs in 2010 × 100

= 30 thousand / 428.5 thousand × 100

= 0.07 × 100

= 7%

Utility's percent Change from 2010 to 2020 = 7%

4 0
3 years ago
Given the preimage and image,find the dilation scale factor.​
Oliga [24]

Answer:

The dilation scale factor is \frac{1}{2}.

Step-by-step explanation:

The image is the dilated form of its preimage if and only if the following conditions are observed:

1) K' = \alpha_{1} \cdot K

2) T' = \alpha_{2} \cdot T

3) P' = \alpha_{3} \cdot P

4) J' = \alpha_{4} \cdot J

5) \alpha_{1} = \alpha_{2} = \alpha_{3} = \alpha_{4}

If we know that K = (2, 0), K' = (1, 0), T = (3, 0), T' = (1.5,0), P = (1, 5), P' = (0.5, 2.5), J = (0, 3) and J' = (0, 1.5), then the coefficients are, respectively:

\alpha_{1} = \frac{1}{2}, \alpha_{2} = \frac{1}{2}, \alpha_{3} = \frac{1}{2}, \alpha_{4} = \frac{1}{2}

As \alpha_{1} = \alpha_{2} = \alpha_{3} = \alpha_{4}, we conclude that the dilation scale factor applied in the preimage is equal to \frac{1}{2}.

7 0
2 years ago
Solve the system of equations. 3x+2y+z=16 4x−y=−5 y+z=11
labwork [276]

Answer:

I have no clue j need more free answer

Step-by-step explanation:

3x+2y+z=16 4x-y=-5 y+x=11

6 0
2 years ago
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