You hope to reach $10,000 savings in 6 years in an account paying 1.5%. What is the present value?
All answers will include a $sign.

Answer:

The area at time t is given  by [tex]A(t) =\pi (4t^2+2t+0.25).[/tex]

Step-by-step explanation:

We know the radius [tex]r(t)[/tex] of the oil spill as a function of time, and we know the area [tex]A(r)[/tex] as a function of radius, and we want the area at time t. In other words we are looking for area as a function of time [tex]A(t)[/tex]

We find [tex]A(t)[/tex] by putting [tex]r(t)[/tex]  into [tex]A(r)[/tex] as a substitute to r:

[tex]A(t) = A(r(t))= \pi r(t)^2 =\pi (0.5 + 2t)^2={\pi (4t^2+2t+0.25).}[/tex]

[tex]\boxed{A(t) =\pi (4t^2+2t+0.25).}[/tex]

Which is our answer.

To find the composite function for the area of the oil spill over time, replace 'r' in A(r) = πr2 with the function r(t). The function becomes A(t) = π(0.5 + 2t)2.

In order to find the function that represents the area of the oil spill over time, we need to write a composite function. This means we plug the function r(t) into A(r). Since r(t) = 0.5 + 2t, you can replace every instance of 'r' in A(r) = πr2 with (0.5 + 2t) to get the area as a function of time 't'. So, the composite function becomes A(t) = π(0.5 + 2t)2. Now we have a composite function that represents the area of the oil spill, denoted by A(t), as a function of time. The function is: A(t) = π(0.5 + 2t)2.

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Answer:

x = 1 , y = 2

Step-by-step explanation:

Solve the following system:

{5 x + 2 = 7 | (equation 1)

y = x + 1 | (equation 2)

Express the system in standard form:

{5 x+0 y = 5 | (equation 1)

-x + y = 1 | (equation 2)

Add 1/5 × (equation 1) to equation 2:

{5 x+0 y = 5 | (equation 1)

0 x+y = 2 | (equation 2)

Divide equation 1 by 5:

{x+0 y = 1 | (equation 1)

0 x+y = 2 | (equation 2)

Collect results:

Answer: {x = 1 , y = 2

Answer:

[tex]\frac{61}{90}[/tex]

Step-by-step explanation:

We require to create 2 equations with the repeated value 7 after the decimal point

Let x = 0.6777777... ← multiply both sides by 10 and 100

10x = 6.777...... → (1)

100x = 67.777..... → (2)

Subtract (1) from (2) thus eliminating the repeating value

90x = 61 ( divide both sides by 60 )

x = [tex]\frac{61}{90}[/tex]

The decimal 0.67 with the repeating 7 can be written as the simplified fraction 2/3.

To rewrite the decimal 0.67 with the repeating 7 as a simplified fraction, we can use the concept of infinite geometric series.

Let x = 0.677777...

Multiply both sides of the equation by 10 to shift the decimal point:

10x = 6.777777...

Now, subtract the original equation from the shifted equation to eliminate the repeating 7s:

10x - x = 6.777777... - 0.677777...

Simplifying, we get:

9x = 6

Divide both sides of the equation by 9 to solve for x:

x = 6/9

The fraction 6/9 can be further simplified by dividing both the numerator and denominator by their greatest common divisor, which is 3:

x = (6/3) / (9/3)

x = 2/3

Therefore, the decimal 0.67 with the repeating 7 can be written as the simplified fraction 2/3.

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Answer:

26 years of age.

Step-by-step explanation:

The average annual income, I, in dollars, of a lawyer with an age of x years is modeled with with the following function:

I = - 425x² + 45500x - 650000 .......... (1)

If the average annual income of the lawyer at the age of x years is $250000, then from the equation (1) we can write

- 425x² + 45500x - 650000 = 250000

⇒ - 425x² + 45500x - 900000 = 0

⇒ - 17x² + 1820x - 36000 = 0

Now, using the quadratic formula,

[tex]x = \frac{- 1820 \pm \sqrt{(1820)^{2} - 4(-17)(- 36000) } }{2(- 17)} = \frac{-1820 + 929.73}{- 34} = 26[/tex] years (Approximate)

{We have neglected the other root as we need the youngest age}(Answer)

Answer: 27

Step-by-step explanation:

Other answer is wrong

Answer:

Step-by-step explanation:

Set this up as a proportion with granola on the top and chocolate chips on the bottom:

[tex]\frac{g}{cc}:\frac{1.75}{\frac{1}{3} }=\frac{x}{1}[/tex] and cross multiply to solve for x:

1/3x = 1.75 Multiply both sides by 3 to get

x = 5.25

This means for every 1 cup of chocolate chips, he needs 5 1/4 cups of granola.

George shovels at a rate of 8.33 square yards per hour. In 5 1/2 hours, he will shovel approximately 45.815 square yards of his driveway.

The student asked about how many square yards of driveway George would shovel in 5 1/2 hours after shoveling 12 2/4 square yards in 1 1/2 hours. To find this, we first need to calculate the rate at which George is shoveling.

George shovels 12 2/4 square yards in 1 1/2 hours. Simplifying these fractions, we have 12.5 square yards in 1.5 hours. The rate is therefore 12.5 ÷ 1.5 yards per hour = 8.33 square yards per hour.

Next, we multiply this rate by the total time George will be shoveling to find how much he would shovel in 5 1/2 hours:

8.33 yards/hour × 5.5 hours = 45.815 square yards

So, George will shovel approximately 45.815 square yards of his driveway in 5 1/2 hours.

Final answer:

To find out how many square yards of driveway George would shovel in 5 1/2 hours, we can set up a ratio using the given information and multiply the rate by the time.

Explanation:

To find out how many square yards of driveway George would shovel in 5 1/2 hours, we can set up a ratio using the given information. In 1 1/2 hours, he shovels 12 2/4 square yards of snow. We can write this as a fraction: 12 2/4 / 1 1/2. To simplify this fraction, we can convert the mixed numbers to improper fractions: 50/4 / 3/2.

To divide fractions, we multiply the first fraction by the reciprocal of the second fraction: (50/4) × (2/3). Multiplying the numerators and denominators, we get (50 × 2) / (4 × 3) = 100/12.

So, in 1 1/2 hours, George shovels 100/12 square yards of snow. To find out how many square yards he would shovel in 5 1/2 hours, we can multiply this rate by 5 1/2: (100/12) × (5 1/2). Multiplying the numerators and denominators, we get (100 × 11) / (12 × 2) = 1100/24. Simplifying this fraction, we get 275/6.

Therefore, George would shovel approximately 275/6 square yards of driveway in 5 1/2 hours.

Answer:

The solution is the ordered pair (3,2)

The graph in the attached figure

Step-by-step explanation:

we have

[tex]y=\frac{1}{3}x+1[/tex] -----> equation A

[tex]x+y=5[/tex] ----> equation B

Solve by graphing

Remember that

The solution of the system of equations is the intersection point both lines

using a graphing tool

The intersection point is (3,2)

see the attached figure

therefore

The solution is the ordered pair (3,2)

A system of equation can be solved in several ways, which includes the use of graphs

The solution to the system of linear equations is (3,2)

The system of equations is given as:

[tex]y=\frac 13x+1[/tex]

[tex]x+y=5[/tex]

See attachment for the graphs of  [tex]y=\frac 13x+1[/tex]  and [tex]x+y=5[/tex].

From the attachment, the point of intersection of the lines of both equations is (3,2)

Hence, the solution to the system of linear equations is (3,2)

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Answer:

20. 3

Step-by-step explanation:

23.6 - 2 × 3 ÷ 2 = 23.6 - 3

                         = 20.3

Answer:

$240

Step-by-step explanation:

i = prt

i = $2,000 x 0.03 x 4

i = $240

The amount of interest Antonia will earn in 4 years is $240.

Answer:

The only correct statement is the first one

because the product of a number greater than 1 and another positive number always makes the second number greater than its original value

:)

Answer: 50%

Step-by-step explanation:

12x1.5=18

Answer:

50% increase

Step-by-step explanation:

Percentage change = increase/original × 100

[tex]change = \frac{(18 - 12)}{12} \times 100[/tex]

[tex]change = \frac{6}{12} \times 100[/tex]

[tex]change = 0.5 \times 100[/tex]

[tex]change = 50\%[/tex]

Answer:

[tex]y=-4x+8[/tex]

Step-by-step explanation:

step 1

Find the slope

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

[tex]m=\frac{y2-y1}{x2-x1}[/tex]

take two points from the data

(0,8), and (8,-24).

substitute

[tex]m=\frac{-24-8}{8-0}[/tex]

[tex]m=\frac{-32}{8}[/tex]

[tex]m=-4[/tex]

step 2

Find the equation of he line in slope intercept form

[tex]y=mx+b[/tex]

we have

[tex]m=-4[/tex]

[tex]b=8[/tex] ----> the y-intercept is given

substitute

[tex]y=-4x+8[/tex]

Answer:

Graph is attached below.

The graph illustrates the music that Jada may have downloaded with the $15 (s)he spent. The x-axis represents the number songs and the y-axis represents the number of albums. The data shows what combination of music she may have downloaded. The number of songs and albums have a negative correlation because if more money is spent on one variable, there is less money available to spend on the other.

Step-by-step explanation:

How to create a graph:

Using the data from part 1, plot the points (6, 3) (22, 1) and (30, 0) onto the graph. Label the x and y axis as the question asks. The axis should have arrows at the end. Include a title for the graph.

Do not connect the points because this indicates that all the space between the points are possible. Connecting the points includes decimal numbers and you can't buy part of a song or album, only a whole song or album.

Answer:

  (-2, 3)

Step-by-step explanation:

f(x) +5 means 5 is added to the y-value that is output from the function. The given point indicates the function output is -2, so when 5 is added, the result is +3. The point (-2, 3) is on the graph of f(x)+5.

Answer:

The required equation models the total profit, y, based on the number of hot dogs sold, x  is   y = 3 x - 30.

Step-by-step explanation:

Let x = total number of hot dogs sold

y = total profit from total sales of hot dogs

The given situation can be written as: y = m x +  C  ......[A]

Now, Profit for 40 hot dogs = $90 profit

So, here this can be written as:

90 = 40 m + C ......[1]

Profit for 80 hot dogs = $210 profit

So, here this can be written as:

210 = 80 m + C ......[2]

Now, solving both the equations, we get:

Subtracting  [1] and [2], we get

210  - 90  = 80 m + C  - (40 m + C)

or, 120 = 40 m

or, m = 120/40 = 3

or, m = 3

Solving for the value of C , we get: C = - 30

Putting the value of m back in the equation : y   = m x + C

y = 3 x -30

Hence, the required equation models the total profit, y, based on the number of hot dogs sold, x  is   y = 3 x - 30.

Answer:

Hence after solving the given equation we get x = 13/20.

Step-by-step explanation:

Given:

-3 x + 0.1 + 10 x = x + 4

-3 x + 10 x - x = 4 - 0.1

6 x = 3.9

x = [tex]\frac{3.9}{6}[/tex]

x = [tex]\frac{1.3}{2}[/tex]

x = [tex]\frac{13}{20}[/tex]

Firstly they are not numbers, they are ordered pairs or points with a form [tex](x,f(x))[/tex] yes they probably lie on a function graph but that would be rather impossible to find out. The function may be linear, exponential, logarithmic etc. we can't tell. All we can tell is that if these ordered pairs [tex]P_{1,2,3}[/tex] lie on a function graph [tex]P_{1,2,3}\in G_f[/tex] where [tex]G_f=\{(x,f(x)):\forall x\in D_f\wedge f(x)\in T_f\}[/tex] where D is definition set of function defined x's and T a transformation set of f(x)'s for this function. So yes they may lie on some lambda function but they themselves are nothing but an ordered pairs with no meaningful connection.

Hope this helps.

Answer:

no

Step-by-step explanation:

there are two coordinates with the same x value

Step-by-step explanation:

making x subject in eq 1

x= (-1-9y)/-14

substituting the value of x in eq 2

17(-1-9y/-14)=7+9y

(-17-153y)/-14=7+9y

-17-153y=-98-126y

-17+98=153y-126y

81=27y

y=3

substituting this value of y in eq 1

-14x=-1-9(3)

-14x=-28

x=2

(x,y) = (2,3)

Answer:

  9 loaves

Step-by-step explanation:

Judy get 3/4 of the bread, so ...

  (3/4) · 12 loaves = 9 loaves

Final answer:

In order to find out how much bread Kendra gives Judy, we can set up a system of equations.

Explanation:

In order to find out how much bread Kendra gives Judy, we can set up a system of equations based on the information given. Let's say Kendra gives Lynn x loaves of bread. According to the problem, Kendra gives Judy 3 times the amount she gives Lynn, so Judy receives 3x loaves of bread. Together, they receive 12 loaves of bread, so x + 3x = 12. Simplifying the equation, we get 4x = 12. Dividing both sides by 4, we find x = 3. Therefore, Kendra gives Judy 3x = 3(3) = 9 loaves of bread.

Answer:

56652.3 ft^3

Step-by-step explanation:

The formula for the volume of a right circular cone is V=13pi*r^2*h where r is the radius of the base.

So V=13pi*(15.6)^2*(5.7)=56652.3

Answer:

Yes, both equations should be true.

Question is Incomplete, Complete question is given below.

Julia exercises at the gym. For every 3 minutes she spends running, she spends 5 minutes lifting weights.

Which of the following could be how Julia spends time at the gym?

A  Run for 10 mins and lifting weights for 12 mins.

B  Run for 15 minutes and lift weights for 25 mins.

C  Run for 20 mins and lift weights for 30 mins.

D  Run for 24 mins and lift weights for 48 mins.

E  Run for 30 mins and lift weights for 50 mins.

Answer:

B  Run for 15 minutes and lift weights for 25 mins.

E  Run for 30 mins and lift weights for 50 mins.

Step-by-step explanation:

Given:

Julia Spend s 3 minute for running and weight lifts for 5 mins.

We need to find which choices are correct match for the given data.

Hence we will check each.

A  Run for 10 mins and lifting weights for 12 mins.

Since given that she runs for 3 mins and in the above choice the given date is she is running for 10 mins it is neither 3 nor multiple of 3.

Hence this is Choice is Incorrect.

B  Run for 15 minutes and lift weights for 25 mins.

Now Given in choice is that she runs for 15 minutes and in given data she runs for 3 minutes hence 15 is multiple of 3 and is multiplied by 5 also given lift weights for 25 mins and in given data she lift weights for 5 mins since 25 is multiple of 5 and is multiplied by 5.

Hence the above Choice is Correct.

C  Run for 20 mins and lift weights for 30 mins.

Since given that she runs for 3 mins and in the above choice the given date is she is running for 20 mins it is neither 3 nor multiple of 3.

Hence this is Choice is Incorrect.

D  Run for 24 mins and lift weights for 48 mins.

Now Given in choice is that she runs for 24 minutes and in given data she runs for 3 minutes hence 24 is multiple of 3 and is multiplied by 8 also given lift weights for 48 mins and in given data she lift weights for 5 mins and 48 is not the multiple of 5.

Hence this is Choice is Incorrect.

E  Run for 30 mins and lift weights for 50 mins.

Now Given in choice is that she runs for 30 minutes and in given data she runs for 3 minutes hence 30 is multiple of 3 and is multiplied by 10 also given lift weights for 50 mins and in given data she lift weights for 5 mins since 50 is multiple of 5 and is multiplied by 10.

Hence the above Choice is Correct.

The given statement written in symbolic language is x = 3y + 4 and x + y = 72 where "x" is the cost of one book and "y" is the cost of another book

Solution:

Given that Bruce bought two books

One book costs $ 4.00 more than three times the other

Let the two books be denoted as Book A and book B

Let "x" be the cost of book A

Let "y" be the cost of Book B

From given,

One book costs $ 4.00 more than three times the other

Let Cost of book A = $ 4.00 more than three times the other book B

x = 4 + 3 times cost of Book B

x = 4 + 3y

x = 3y + 4 --- (i)

Also given that Together, the two books cost him $72

cost of book A + cost of Book B = 72

x + y = 72 ------- (ii)

Therefore the given statement written in symbolic language is:

x = 3y + 4 and x + y = 72

Answer:

see below

Step-by-step explanation:

*I'm not sure what you mean when to add and subtract but I hope this helps!

Answer:

Triangle1: 13

Triangle2: 25

Triangle3: 17

Step-by-step explanation:

*Pythagorean Theorem Formula: a²+b²=c² where c is the hypotenuse (the side opposite of the right angle)

Triangle1:

1. Plug in the values into the Pythagorean Theorem Formula and simplify as shown below.

  5²+12²=c²

  25+144=c²

  169=c²

  c=√169

  c=13

Triangle2:

1. Plug in the values into the Pythagorean Theorem Formula and simplify as shown below.

  15²+20²=c²

  225+400=c²

  625=c²

  c=√625

  c=25

Triangle3:

1. Plug in the values into the Pythagorean Theorem Formula and simplify as shown below.

  8²+15²=c²

  64+225=c²

  289=c²

  c=√289

  c=17

Answer:

23 points

Step-by-step explanation:

If he shane scored 3 fewer points, then that means double of Jason's score is 56. divide 56 by two to get Jason's real score, which is 23.

Answer:

238°

Step-by-step explanation:

In a cyclic quadrilateral, the pair of opposite angles add up to 180 degrees.

So, the angle "21x - 2" and the angle "38x + 5"  add up to 180.

So, we can write an equation and solve for x first:

[tex]21x-2+38x+5=180\\59x+3=180\\59x=180-3\\59x=177\\x=3[/tex]

x = 3

Now, Arc FGH is DOUBLE of Angle A. Angle A is "38x + 5". We know x, so angle A is:

Angle A = 38x + 5 = 38(3) + 5 = 119

Thus, Arc FGH = 2 * 119 = 238°

The number of unripe apples in a sack, given that there are N total apples and 3 are ripe, is calculated by subtracting 3 from N (N - 3).

The question posed is asking for a basic subtraction calculation within the context of ripe and unripe apples.

Given that there are N apples in total and 3 of them are ripe, we need to find out how many are not ripe.

The number of not ripe apples is N - 3, where N is the total number of apples in the sack.

To solve this, we subtract the number of ripe apples from the total number of apples:

For example, if a sack has 10 apples and 3 are ripe, then there would be 10 - 3 = 7 unripe apples.

Number of adult tickets sold is 100 and number of children tickets sold is 150

Solution:

Let "c" be the number of childrens ticket sold

Let "a" be the number of adult tickets sold

Cost of 1 children's musical ticket = $ 2.00

Cost of 1 adult musical ticket = $ 3.50

Given that 250 tickets were sold

number of childrens ticket sold + number of adult tickets sold = 250

c + a = 250 ---- eqn 1

250 tickets were sold for a total of 650

So we can frame a equation as:

number of childrens ticket sold x Cost of 1 children's musical ticket + number of adult tickets sold x Cost of 1 adult musical ticket = 650

[tex]c \times 2.00 + a \times 3.50 = 650[/tex]

2c + 3.50a = 650 ---- eqn 2

Let us solve eqn 1 and eqn 2 to find values of "a" and "c"

From eqn 1,

c = 250 - a ----- eqn 3

Substitute eqn 3 in eqn 2

2(250 - a) + 3.50a = 650

500 - 2a + 3.50a = 650

1.5a = 150

From eqn 1,

c = 250 - 100

Thus number of adult tickets sold is 100 and number of children tickets sold is 150