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Airida [17]
2 years ago
8

Kathy and Mark Smith believe investing in their retirement is critical. Kathy began investing 20% of each paycheck in a retireme

nt account when she was 20 years old. She has saved four times more than Mark who began saving when he was 35. If their total retirement savings equals $1,530,000, how much are Kathy’s and Mark's investments worth?

Mathematics
1 answer:
Alona [7]2 years ago
5 0

Answer:

Kathy: $1,224,000

Mark: $306,000

Look at the attachment

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A line passes through the points (p, a) and (p, –a) where p and a are real numbers and p ≠ 0. Describe each of the following. Ex
MissTica

Answer:

Part A) The slope is undefined

Part B) The equation of the line is x=p

Part C) None y-intercept

Part D) The slope of a line perpendicular to the given line is equal to zero

Step-by-step explanation:

we have that

Describe

A) slope of the line

B) equation of the line

C) y-intercept

D) slope of a line perpendicular to the given line

Part A) slope of the line

we know that

The formula to calculate the slope between two points is equal to

m=\frac{y2-y1}{x2-x1}

we have

(p,a)\ (p,-a)

Substitute the values

m=\frac{-a-a}{p-p}

m=\frac{-2a}{0}  -----> the slope is undefined

Its a vertical line (parallel to the y-axis)

Part B) Equation of the line

we know that

The equation of a vertical line is equal to the x-coordinate of the points through which the line passes.

so

x=p

Part C) The y-intercept

The y-intercept is the value of y when the value of x is equal to zero

The vertical line not intercept the y-axis

so

None y-intercept

Part D) slope of a line perpendicular to the given line

A line perpendicular to the given line is a horizontal line (parallel to the x-axis)

therefore

The slope is equal to zero

6 0
2 years ago
Select the correct interpretation of the probability of getting an 11 when a pair of dice is rolled. Interpret an event as signi
klio [65]

Answer:

c. Not significant at .055

Step-by-step explanation:

When a pair of dice is rolled, we have 6²=36 possible outcomes. Only 2 of these outcomes have a total score of 11:

  1. When the first dice is 5 and the second is 6.
  2. When the first dice is 6 and the second is 5.

Then, we can calculate the probability of getting 11 as the quotient between the successs outcomes and the total outcomes.

Then, the probability of getting 11 is:

P=\dfrac{X}{N}=\dfrac{2}{36}=0.055

This probability is not equal or less than 0.05, so it is not significant at 0.055.

3 0
2 years ago
Preston is making cookies. He has fraction 4 over 5 cup of flour in a bag. He then used two fraction 1 over 10 cup scoops of flo
Art [367]

I'm pretty sure the answer will be 6/10





Hope this helps, best of luck, terribly sorry if I'm wrong if I am my  apologies




~Animaljamissofab ♥

5 0
2 years ago
Read 2 more answers
A teacher decides to purchase a new car and considers two options. Option one is the new Zoomba for $60,000 with an expected dep
kupik [55]

Answer:

She chose Option 2 which is a linear option, because it offers a smaller lose    

in value compared to option 1 which is an exponential option.

The final value for option 2=$32,800

Step-by-step explanation:

Option 1

New Zoomba for 60000 with a depreciation rat of 2%per month for 3 years

Exponential equation;

y=a(1-r)^t

where;

y=future value

a=initial value=60000

r=depreciation rate=2% per month

t=time interval=12×3=36 months

Replacing;

y=60000(1-2/100)^36

y=60000(0.98)^36=28,992.79

The value after 3 years=$28,992.79

Initial value-Final value=(60000-28992.79)=$31007.21

Percentage of initial value lost=((Final value-Initial Value)/(Initial Value))×100

(31007.21/60000)×100=51.68%

Option 2

New starfish for $40,000 with a depreciation of $200 per month for 3 years

Linear equation;

y=a-bt

where;

y=Future value

a=Initial value=$40,000

b=the depreciation amount per time interval=$200 per month for 3 years

t=time interval=(3×12)=36 months

Replacing;

y=40000-(200×36)

y=32,800

Final value=y=$32,800

Initial value-Final value=(40000-32800)=$7200

Percentage of initial value lost=((Final value-Initial Value)/(Initial Value))×100

(7200/40000)×100=18%

Option 1(51.68%)>Option 2(18%) therefor Option 1 loses value at a faster rate than Option 2

She chose Option 2 which is a linear option, because it offers a smaller lose    

in value compared to option 1 which is an exponential option

4 0
2 years ago
∆ABC has vertices at A(12, 8), B(4, 8), and C(4, 14). ∆XYZ has vertices at X(6, 6), Y(4, 12), and Z(10, 14). ∆MNO has vertices a
koban [17]
To get the length of each side,
use the distance formula with equation: 
Distance = ((x2-x1)^2+(y2-y1)^2)^0.5 
Solving
<span>AB = 8 units   BC = 6 units AC = 10 units
</span><span>MN =8units    NO = 6 units MO = 10 units
</span><span>XY = 6.32 units   YZ = 6.32 units XZ = 8.94 units
</span>JK = 4.47 units    KL = 4.47 units JL = 6 units 

1 The right answer is the letter b) triangle ABC and Triangle MNO are Congruent <span>triangles
ABC and MNO  are triangles that have the same lengths of its three sides.

</span>2 The answer is the letter c) rotation
There is a rotation of 90º about ABC and MNO the origin is B=N
B=N
C----------O
A----------M
3 0
2 years ago
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