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Rainbow [258]
2 years ago
13

Divide the given question:

t="12.36 \div 0.9" align="absmiddle" class="latex-formula">
​
Mathematics
1 answer:
Marina CMI [18]2 years ago
3 0

12.36 \div 0.9 = 13.73

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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
Pls help urgently extra points and mark brainlist
tankabanditka [31]

Answer:

(3+2)×5= 5 power 2

5 power 3= 125

10 power 2 over 2= 50

Step-by-step explanation:

6 0
2 years ago
A damsel is in distress and is being
Katen [24]

Answer:

30 feet

Step-by-step explanation:

Let x be the length of the ladder. Then, x cos(60) = 15

If we divide both sides by cos(60), then x = 30 feet.

6 0
2 years ago
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How many sevenths are there in two wholes?
schepotkina [342]

Answer:

14

Step-by-step explanation:

7 times 2 = 14

7 0
2 years ago
Find the coordinates of the midpoint M of the segment with the given endpoints. Then find the distance between the two points. R
Mrac [35]

Answer:

Midpoint (-2,4)

distance nearest tenth = 8.9

The approximate distance = 9

Step-by-step explanation:

Formulas

PQ midpoint = (x2 + x1)/2, (y2 + y1)/2

distance d = sqrt( (x2 - x1)^2 + (y2 - y1)^2 )

Givens

x2 = -4

x1 = 0

y2 = 1

y1 = 7

Solution

M(PQ) = (-4+0)/2, (1 + 7)/2

M(PQ) = -2, 4

The midpoint is -2,4

The distance = sqrt( (4 - 0)^2 + (1 + 7)^2 )

The distance = sqrt(16 + 64)

The distance = sqrt(80)

The distance = 4√5           exactly

The distance = 8.94    

The distance = 8.9            To the nearest tenth

Question 2

The distance is rounded to the nearest whole number which is 9.

6 0
3 years ago
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