Can you guys help me solve this ?

Data: John's current pay is $78,000. Annual salary increase rate: 5% Maximum 401k contribution: 15% of pre-tax gross yearly salary Every year, John intends to pay 10% of his current earnings to his 401k.

Annual compounded return on 401k investments is expected to be 8%.

$10,000 wedding money target in 12 months

Short-term CD interest rate: 2%

Goal for house down payment: $40,000 in 5 years

Annual expected return on housing fund investments: 4%

At the age of 60, your 401k balance is $1,000,000.

85 years is the average life expectancy.

0.5% (6%/12) monthly rate of return on retirement investments

To figure out John's 401k balance at age 60, do the following:

Compute John's annual contribution to his 401k: $78,000 x 10% = $7,800

Employ the financial calculator's future value (FV) function:

N (number) = 30  (number of years until retirement)

I/Y = 8% (annual rate of return)

PMT = -$7,800 (negative because it’s a cash outflow)

PV = 0 (no initial balance)

FV = $?

FV = $1,057,323.95

Therefore, John would have saved approximately $1,057,323.95 at age 60.

a) To achieve an age 60 balance of one million dollars:

Use the present value (PV) function on the financial calculator:

N = 30 (number of years until retirement)

I/Y = 8% (annual rate of return)

PMT = -$? (negative because it’s a cash outflow)

PV = 0 (no initial balance)

FV = $1,000,000

PMT = -$9,308.79

Therefore, John would have to save approximately $9,308.79 every year to achieve an age 60 balance of one million dollars.

b) To find the percentage of his current salary that the annual savings amount represents: Divide the annual savings amount by John’s current salary: $9,308.79 / $78,000 = 0.1194

Multiply by 100 to get the percentage: 0.1194 x 100 = 11.94%

Therefore, the annual savings amount represents approximately 11.94% of John’s current salary.

To calculate how much John will have to contribute to the wedding fund every month for the next 12 months:

Use the present value (PV) function on the financial calculator:

N = 12 (number of monthly deposits)

I/Y = 2%/12 = 0.1667% (monthly rate of return)

PMT = -$? (negative because it’s a cash outflow)

PV = 0 (no initial balance)

FV = $10,000

PMT = -$821.47 As a result, John will have to contribute $821.47 to the wedding fund each month for the following 12 months.

To determine how much John must save each month for the next 60 months in order to acquire $40,000:

Employ the financial calculator's future value (FV) function:

N = 60 (number of months) (number of months)

I/Y = 4%/12 = 0.3333% (monthly interest rate)

PMT = -$? (negative since it represents a monetary outflow)

PV = 0 (no starting balance) (no initial balance)

FV = $40,000

PMT = -$603.94

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The volume of the solid obtained by rotating the region in the first quadrant bounded by x=0, y=1, x=y^4 about the line y=10 is 678.53 units cubed.

Here we can use the formula for the area of the circle which is A = pi*r^2 to calculate the area of the cylindrical shell. since the volume of the solid formed by rotating the given region about the line y=10 can be found by using the method of cylindrical shells, it states that the volume of the solid of revolution is equal to the integral of the cross-sectional area of the solid with respect to the axis of rotation.

in order to calculate the volume, we first need to find the radius of the cylindrical shell, this can be done by subtracting the distance from the line of rotation. in this case, the distance from the line of rotation to the axis of rotation is 10, thus the radius of the cylindrical shell is y-10.

while using the formula for the area of the circle, here subsituting the radius of the cylindrical shell into this formula will give us the area of the sylindrical shell, then integrate the area of the cylindrical shell with respect to the axis of  rotation,  which will given us the volume of the solid, so the volume of the solid  by rotating the region in the first quadrant bounded by  v about the line  y=10 given by the integral of the I*(y-10)^2 from y=1 to y=10, which gives  us the aprroximately 678.54

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The area of the shaded region is  104 cm²

First, we need to know that the area of a circle is calculated using the formula;

A = πr²

Such that the parameters of the formula are;

First, let us find the area of the small circle

Area = 3.14 × 4²

Find the square value and multiply, we have;

Area = 50.24cm²

Area of the large circle = 3.14 × 7²

Find the square value and multiply

Area = 153. 86cm²

Area of the shaded region = Area of large circle - area of small circle

= 153.86 - 50.24

= 104 cm²

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According to the information, we can infer that the correct expression is (10 * 7) + (2 * 7) (option D).

To find the correct expression we must look at the graph and interpret the information it has. In this case, some tiles are white and others are gray, so they would represent different elements. In this case, the white area is 10 * 7 tiles, so this would be the first part of the expression.

On the other hand, the second part of the expression would be 7 * 2, which represents the length, length and width of the gray area. According to the above, the correct expression would be (10 * 7) + (2 * 7), the first part in parentheses represents the white area and the second part in parentheses represents the gray area.

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Answer:

Step-by-step explanation:

16

Answer:

16%

Step-by-step explanation:

Trust

When Henry ran 1 5/8 miles in the morning and 9/10 miles in the afternoon, In all he a total of 2 21/40 miles

The number of miles Henry ran is calculated by addition operation

The sum of the miles Henry ran in the morning plus the number of miles he ran in the afternoon gives the what Henry ran in all

The procedure involves addition of tractions and done as follows

= 1 5/8 + 9/10

= 13/8 + 9/10

adding both fractions will result to

= 101/40 miles

= 2 21/40 miles (as a mixed number)

Henry ran a sum of 2 21/40 miles

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The values into the slope-intercept form, we have y = -5x - 6

The slope-intercept form of a linear equation is given by:

y = mx + b

where 'm' represents the slope of the line, and 'b' represents the y-intercept.

In this case, the y-intercept is (0, -6), which means that the line crosses the y-axis at the point (0, -6).

The slope is given as -5.

Therefore, substituting the values into the slope-intercept form, we have:

y = -5x - 6

This equation represents the line with a y-intercept of (0, -6) and a slope of -5.

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The difference between the selling price and the cost price is the profit he earned.

Profit = Selling Price - Cost Price

Profit = $216 - $180

Profit = $36

To find the percentage profit, we need to calculate what proportion of the cost price the profit represents, and express that as a percentage :

Percentage Profit = (Profit : Cost Price) * 100%

Percentage Profit = ($36 : $180) * 100%

Percentage Profit = 0.2 * 100%

Percentage Profit = 20%

Therefore, his percentage profit is 20%.

Answer:

5 3/4 bakers can make 27.91 pretzels in 1 1/2 hours.

Step-by-step explanation:

Given that 1/3 of 33 bakers can make 89 pretzels in 2 1/2 hours, to determine how many pretzels can 5 3/4 bakers make in 1 1/2 hours the following calculation must be performed:

33 x 1/3 = 11

11 bakers can make 89 pretzels in 2.5 hours, that is, 35.6 per hour (89 / 2.5), and 3,236 per baker per hour (35.6 / 11).

3/4 = 0.75

Therefore, 5.75 bakers, making 3.236 per hour during 1.5 hour, will make the following amount of pretzels:

3.236 x 1.5 x 5.75 = X

4.854 x 5.75 = X

27.91 = X

Therefore, 5 3/4 bakers can make 27.91 pretzels in 1 1/2 hours.

Answer:

d = 5 is a solution to the equation 13 - d = 8

Step-by-step explanation:

We have to solve 13 - d = 8

Now,

13 - d = 8,

We add d on both sides,

13 - d + d = 8 + d

13 = 8 + d

we subtract 8 from both sides,

13 - 8 = 8 - 8 + d

5 = d

d = 5

Hence the answer is 5

Answer:

no solutions

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

equation of blue line is y = x + 2 , in slope- intercept form

with slope m = 1

equation of red line is y = x - 3 , in slope- intercept form

with slope m = 1

• Parallel lines have equal slopes

then the blue and red lines are parallel.

the solution to the system is at the point of intersection of the 2 lines

since the lines are parallel then they do not intersect each other.

thus the system shown has no solution.

a) The inequality for the expression 2z + 9 is 2z + 9 > 13.

b) The inequality for the expression 3(z - 4) is 3z - 12 > -6.

c) The inequality for the expression 4 + 2z is 4 + 2z > 8.

d) The inequality for the expression 5(3z - 2) is 15z - 10 > 20.

a) To write an inequality for the expression 2z + 9, we can multiply the given inequality z > 2 by 2 and then add 9 to both sides of the inequality:

2z > 2 * 2

2z > 4

Adding 9 to both sides:

2z + 9 > 4 + 9

2z + 9 > 13

Therefore, the inequality for the expression 2z + 9 is 2z + 9 > 13.

b) For the expression 3(z - 4), we can distribute the 3 inside the parentheses:

3z - 3 * 4

3z - 12

Since we are given that z > 2, we can substitute z > 2 into the expression:

3z - 12 > 3 * 2 - 12

3z - 12 > 6 - 12

3z - 12 > -6

Therefore, the inequality for the expression 3(z - 4) is 3z - 12 > -6.

c) The expression 4 + 2z does not change with the given inequality z > 2. We can simply rewrite the expression:

4 + 2z > 4 + 2 * 2

4 + 2z > 4 + 4

4 + 2z > 8

Therefore, the inequality for the expression 4 + 2z is 4 + 2z > 8.

d) Similar to the previous expressions, we can distribute the 5 in the expression 5(3z - 2):

5 * 3z - 5 * 2

15z - 10

Considering the given inequality z > 2, we can substitute z > 2 into the expression:

15z - 10 > 15 * 2 - 10

15z - 10 > 30 - 10

15z - 10 > 20

Therefore, the inequality for the expression 5(3z - 2) is 15z - 10 > 20.

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Answer:

Undefined

Step-by-step explanation:

This equation is just a vertical line, so the slope is undefined.

The equation y² - y²x = 6  can be describe as a function of x as:

y = √(6/(x - x)).

A function is a relationship between inputs where each input is related to exactly one output.

Example:

f(x) = 2x + 1

f(1) = 2 + 1 = 3

f(2) = 2 x 2 + 1 = 4 + 1 = 5

The outputs of the functions are 3 and 5

The inputs of the function are 1 and 2.

We have,

y² - y²x = 6

Taking y² as common.

y²(1 - x) = 6

Divide both sides with (1 - x).

y² = 6/(1 - x)

Square root on both sides.

y = √(6/(x - x))

This is a function of x.

Thus,

y = √(6/(x - x)) is a function of x.

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Answer:

C.

Explanation:

We can answer the question if we graph some points of both functions f(x) and h(x). So, we can use the following table:

x f(x) h(x)

-1 |-1| = 1 2|-1| = 2

0 |0| = 0 2|0| = 0

1 | 1 | = 1 2 | 1 | = 2

So, we can graph both functions as:

Therefore, the answer is C.

It's A

have to get 20 characters.

Answer:

x = 138

Step-by-step explanation:

A straight line is 180

x+ 42 = 180

X = 180-42

x = 138

keeping in mind that parallel lines have exactly the same slope, let's check for the slope of the equation above

\(y=\stackrel{\stackrel{m}{\downarrow }}{-\cfrac{1}{3}}x+7\qquad \impliedby \qquad \begin{array}{|c|ll} \cline{1-1} slope-intercept~form\\ \cline{1-1} \\ y=\underset{y-intercept}{\stackrel{slope\qquad }{\stackrel{\downarrow }{m}x+\underset{\uparrow }{b}}} \\\\ \cline{1-1} \end{array}\)

so we're really looking for the equation of a line whose slope is -1/3 and that it passes through (-2 , 5.5)

\((\stackrel{x_1}{-2}~,~\stackrel{y_1}{5.5})\hspace{10em} \stackrel{slope}{m} ~=~ - \cfrac{1}{3} \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{5.5}=\stackrel{m}{- \cfrac{1}{3}}(x-\stackrel{x_1}{(-2)}) \implies y -5.5= -\cfrac{1}{3} (x +2)\)

\(y-5.5=-\cfrac{1}{3}x-\cfrac{2}{3}\implies y=-\cfrac{1}{3}x-\cfrac{2}{3}+5.5\implies y=-\cfrac{1}{3}x-\cfrac{2}{3}+\cfrac{55}{10} \\\\\\ y=-\cfrac{1}{3}x-\cfrac{2}{3}+\cfrac{11}{2}\implies {\Large \begin{array}{llll} y=-\cfrac{1}{3}x+\cfrac{29}{6} \end{array}}\)

The weight before the party could be any positive number

The weight of the bag of ice after the party was 7/8 pounds. So we can set up an equation:

x - weight used at the party = 7/8

We know that the weight used at the party is the weight before the party minus the weight after the party.

So we can substitute 3x for the weight before the party:

3x - (7/8) = weight used at the party

We don't know the exact weight used at the party, but we do know that it was less than or equal to the weight before the party.

So we can set up another inequality:

weight used at the party ≤ 3x

Putting it all together:

3x - (7/8) ≤ 3x

Simplifying:

-(7/8) ≤ 0

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Answer:

\(y=-\frac 4 3 x+1\)

Step-by-step explanation:

Slope intercept form comes in this format: y= mx+b.

Let's convert it.

\(4x+3y=3\\3y=-4x+3\\y=-\frac 4 3 x+1\)

In conclusion the answer is y = -4/3x+1

It will take approximately 25 hours and 1 minute for there to be 150mg of aspirin left in the bloodstream.

We have,

To determine how long it will take for there to be 150mg of aspirin left in the bloodstream, we can use the concept of half-life.

The half-life of aspirin is given as 6 hours, which means that after every 6 hours, the amount of aspirin in the bloodstream reduces by half.

Let's calculate the number of half-lives required to reach 150mg:

Initial amount of aspirin = 625mg

Final amount of aspirin = 150mg

625mg / 150mg = 4.17

This means it will take approximately 4.17 half-lives for the amount of aspirin in the bloodstream to reduce from 625mg to 150mg.

Since each half-life is 6 hours, we can calculate the total time it will take:

Total time = Number of half-lives * Half-life duration

Total time = 4.17 x 6 hours

Total time ≈ 25 hours and 1 minute

Therefore,

It will take approximately 25 hours and 1 minute for there to be 150mg of aspirin left in the bloodstream.

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Answer:

18 Bowls of Candy

Step-by-step explanation:

Camila has 6 bags of candy, and she can pour 1/3 of a bag into a bowl. To determine how many bowls of candy she can make in total, we need to divide the total amount of candy by the amount of candy per bowl.

Since Camila can pour 1/3 of a bag into a bowl, it means she can make 3 bowls of candy with a full bag.

Now, we can calculate the total number of bowls of candy:

Total bowls of candy = (Number of bags) x (Bowls per bag)

Total bowls of candy = 6 bags x 3 bowls per bag

Total bowls of candy = 18 bowls

Therefore, Camila can make a total of 18 bowls of candy with her 6 bags of candy.

Answer:

$102

Step-by-step explanation:

Answer:

6:4 ratio you just put the numbers together

Answer:157.5

Step-by-step explanation:becuase mutilpy 4.5x35 that equals 157.5

Answer: a = -2

Step-by-step explanation:

8a = -12 + 2a

8a - 2a = -12
6a = -12
a = -12/6

a = -2

Answer:

What's the graph?

Step-by-step explanation:

Answer:

47/7

Step-by-step explanation:

6 5/7

=6×7+5/7

=47/7

The value of improper fraction is, 47/7.

The number is expressed as a quotient in which the numerator is divided by the denominator is called fraction.

We have to given that;

The fraction is,

⇒ 6 5/7

Now, We can write the improper fraction as;

⇒ 6 5/7

⇒ (6×7 + 5) / 7

⇒ 47 / 7

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