John inherited $5,000 from his grandfather. He put it in a savings account to buy a car when he turns 16. John is 13 right now. If his savings account earns 7% over the next 3 years, how much interest will he have earned?

Answer:

C.) [tex]7,854[/tex] [tex]cm^2[/tex]

Step-by-step explanation:

use the area of a circle formula:

[tex]A=\pi r^2[/tex]

Insert the radius:

[tex]A=\pi *50^2[/tex]

Simplify exponents:

[tex]A=\pi *2500[/tex]

Simplify pi:

[tex]A=3.14*2500\\A=7850[/tex]

Option C is the closest to 7850.

Finito.

Answer:

Frank, Vanessa, Lois have 34, 17, 64 disks respectively

Step-by-step explanation:

In this question, we are to calculate the number of disks each of the 3 has.

Let the number of disks owned by Frank be x

for vanessa, she has half of what frank has and that would be x/2

Lois has 4 less than 2 times what Frank has, that would be 2x - 4

adding the 3, we have a total of 115 disks

This means that;

x + x/2 + (2x-4) = 115

Multiply throughout by 2;

that gives;

2x + x + 4x - 8 = 230

7x -8 = 230

7x = 230+ 8

7x = 238

x = 238/7

x = 34 disks

Frank has 34

Vaness has 34/2 = 17

Lois have 2x - 4 = 2(34) - 4 = 68 - 4 = 64 disks

Answer:

So Frank has 34 CDs, Vanessa has 17 CD's and Lois has 64 CDs

Step-by-step explanation:

Let's call the amount of CDs that Frank has by 'F', that Vanessa has by 'V' and that Lois has by 'L'. Then, we can write the following equations:

F = 2*V

L = 2*F - 4

F + V + L = 115

If we use the values of F and L in the third equation, we have that:

2*V + V + 2*(2*V) - 4 = 115

7*V = 119

V = 17 CD's

Now we can find F:

F = 2*V = 34 CDs

And then we find L:

L = 2*F - 4 = 68 - 4 = 64 CDs

So Frank has 34 CDs, Vanessa has 17 CD's and Lois has 64 CDs

Answer:

You give it a nudge and it solves itself.

Step-by-step explanation:

Answer: Here is an example.

Step-by-step explanation:

Given: parallelogram ABCD, sides as marked.

Find AD.

Solution: 6x - 10 = 3x + 5 (opposite sides)

3x - 10 = 5;    3x = 15;    x = 5

AD = 4x - 5 = 4(5) - 5 = 15

 Remember:

• This is where the properties of a parallelogram are needed. You know the opposite sides of a parallelogram are congruent, so set the opposite sides equal to one another.

• Be sure to pair up the opposite sides correctly. The side labeled 4x - 5 will not be used when solving for x, but will be used to solve for AD.

Answer:

$13,060.99

Step-by-step explanation:

We can use the following formula to solve:

[tex]A=P(1-r)^t[/tex]

P = principal value

r = rate (decimal)

t = time (years)

First, change 9% into a decimal:

9% -> [tex]\frac{9}{100}[/tex] -> 0.09

Now, just plug the values into the equation:

[tex]A=23,000(1-0.09)^6[/tex]

[tex]A=13,060.99[/tex]

The value of the car after 6 years will be $13,060.99

Answer: 1: 3x

2: area

3: six

4: 3/2

Step-by-step explanation:

The height of the pyramid can be represented as 3x, The area of the hexagon base is six times the area of the equilateral triangle, and the volume is 3/2 times √3 x³.

The pyramid has a hexagonal base with six isosceles triangular faces known as a hexagonal base pyramid. It is also called a heptahedron.

We have,

The length of the base edge of a pyramid = x units

The height of the pyramid is three times longer than the base edge ie.

The height of the pyramid = 3x

The area of an equilateral triangle with base length x units is [tex]\rm x\sqrt{3}[/tex] square units square(let's assume)

Then the area of the hexagon base = 6×[tex]\rm x\sqrt{3}[/tex] ⇒  6[tex]\rm x\sqrt{3}[/tex] square units.

Because the hexagon base has a six-equilateral triangle.

Let's assume the area of a hexagonal base is Y times the equilateral triangle.

[tex]\rm 6x\sqrt{3} = Y \times x\sqrt{3}[/tex]

Y = 6 times

We know the volume of a hexagonal pyramid = [tex]\frac{\sqrt{3} }{2} a^2h[/tex]

Where a is the base length and h is the height of the hexagonal pyramid.

Here a = x units and h = 3x units

Then Volume:

[tex]\frac{\sqrt{3} }{2} x^2(3x)\\\\\frac{{3} }{2} \sqrt{3}x^2[/tex]

Thus, the height of the pyramid can be represented as 3x, The area of the hexagon base is six times the area of the equilateral triangle, and the volume is 3/2 times √3 x³.

Learn more about the pyramid here:

https://brainly.com/question/17615619

Answer:

9

[tex] {9}^{8} [/tex]

Answer:

B) -4

Step-by-step explanation:

(5/2)x + y = 2

x + (2/3)y = 4

y = 2 - (5/2)x

x + (2/3)(2 - (5/2)x) = 4

x + 4/3 - (5/3)x = 4

(-2/3)x = 8/3

-2x = 8

x = -4

Answer:

  A)  dV/dt=-1.2x^2

Step-by-step explanation:

The rate of change of volume is given by dV/dt. Surface area is proportional to x^2. Since the volume is decreasing, the constant of proportionality between surface area and rate of volume change will be negative. Hence a possible equation might be ...

  dV/dt = -1.2x^2

Answer:

C

Step-by-step explanation:

V(t) = [x(t)]³

A(t) = 6[x(t)]²

dV/dt = k × 6[x(t)]²

Where k < 0

From the options,

taking k = -0.2

dV/dt = -1.2[x(t)]²

Answer: 1:21

Step-by-step explanation:

We know that if they say students they mean both boys and girls so we add 11 and 10 to make 21 and since its, (COACH,) and then student we do 1:21 and not 21:1!

1/21

Step-by-step explanation:

First we need to figure out how many students are in the class.

10 + 11 = 21

Then we need to make a ratio

1/21

For every 21 students there is 1 coach

If you look at the question it says from coach to students so we do 1 coach to 21 students which is why 21/1 is wrong

Hope this helps can I have brainliest

Answer:

$18 is the cost per ticket ordered

Step-by-step explanation:

We proceed as follows;

Let the cost per ticket be $x while the fixed fee be $y

For the person that ordered 5 tickets, we can have his mathematical representation as;

5(x) + y = 93 •••••••••(i)

For the person that ordered 3 tickets, we can have his mathematical representation as;

3(x) + y = 57 ••••••••(ii)

From the first equation, we can have;

y = 93 - 5x

Let’s plug this into ii

3x + 93 - 5x = 57

-2x = 57 -93

2x = 36

x = 36/2

x = $18

This means that the cost per ticket ordered is $18

Answer:

490mph and 510mph

Step-by-step explanation:

Let x mph and x+20 mph be the speeds of the planes. The rate at which their distance from each other increases will be the sum of their speeds which is 2x+20 mph.

Their distance from each other after three hours is ( 1.5 hours)*(2x+20 mph) = 3x+30 miles. We are given that this is 1500 miles so we can solve for x.

3x+30 = 1500

3x = 1500 - 30

3x = 1470

x = 1470/3

x = 490mph

For the second jet :

x +20 = 490+20

x = 510

Thus the speeds of the two planes are 490 mph and 510mph.

Answer:

510 miles

Step-by-step explanation:

Please kindly check the attached file for explanation.

Answer:

1,000,000

Step-by-step explanation:

Because you are rounding down because it is not enough to round up.

Two polygons are congruent if they are the same size and shape

The soldiers used 562 cartridges in combat, while the subofficers used 138, using the total amount of ammunition and the difference between cartridges used.

The total amount of ammunition for the section is 175 per soldier for a total of 20 soldiers, so we have 175 * 20 = 3500 cartridges. A fifth of this ammunition is used in combat, that is, 3500/5 = 700 cartridges. According to the question, the number of cartridges used by the soldiers exceeds that of the subordinates by 424 cartridges, so we can establish a system of equations:

We can then solve this system and find that the soldiers used 562 cartridges and the subofficers used 138.

https://brainly.com/question/35467992

#SPJ2

Answer: 514.4

Step-by-step explanation:

10, 288 x 5 ÷ 100

Answer:

It is a combination answer

495 ways

Step-by-step explanation:

In this question, we are tasked with calculating the number of ways in which a manager can select 4 people out of 12 for the Sunday evening shift.

Firstly, the question talks about selecting a particular number from a mix, this is a combination question since the key word SELECT is mentioned.

Now, how do we go about it? To select a partial number from a mix , we use the combination formula as stated.

Mathematically, say we are selecting a number r from a total of numbers n, the number of ways we can do this is nCr = n!/(n-r)!r!

In this case however, we are simply selecting 4 out of 12

Our combinational equation thus becomes 12C4 = 12!/(12-4)!4! = 12!/8!4! = 495 ways

Final answer:

The manager can choose 4 from 12 employees in 495 different ways for the Sunday evening shift, using a combination rather than a permutation since the order of selection does not matter.

Explanation:

To determine the number of ways the manager can choose 4 out of 12 employees for the Sunday evening shift, we need to decide whether the order in which the employees are chosen matters. If the order does not matter, we will use a combination. If the order does matter, we would use a permutation. In this case, because the task is simply to choose 4 employees and the order in which they are chosen does not affect the outcome, we use a combination.

The formula for finding the number of combinations when choosing k objects out of a total of n objects without repetition is given by:

C(n, k) = n! / (k! * (n-k)!)

In this situation, we have n=12 and k=4, so we calculate:

C(12, 4) = 12! / (4! * (12-4)!) = 12! / (4! * 8!) = (12*11*10*9) / (4*3*2*1) = 495

Therefore, there are 495 different ways for the manager to choose 4 employees for the Sunday evening shift.

Answer:2(B) and 4(D) are your answers!!

Step-by-step explanation:

hope this helped youu!!have a terrific Tuesday!

Answer:

11/32

Step-by-step explanation:

4/16 + 2/16 - 1/32

simplify and solve

Answer:

the ratio is 2:9

Step-by-step explanation:

there are a total of 9 flowers, she planted 2 daisies

Answer 3.5 inches

Step-by-step explanation:

Answer:

A. 3.5

Step-by-step explanation:

Answer:

48

Step-by-step explanation:

6*5+6*3=30+18=48

distubutive property

Answer:

1. M = C*1.018^t

After 15 years: M = 4965.93

2. After 3 years: M = 2249.728

After 18 years: M = 4051.633

Time to achieve 3000: t = 10.338 years

Step-by-step explanation:

1. Since the money gets increased every year at a rate of 1.8% after one year it'll be the initial amount multiplied by 1.018, so:

After one year:

M = C*1.018

After two years:

M = C*1.018*1.018 = C*(1.018)²

After three years:

M = C*(1.018)²*1.018 = C*(1.018)³

And so on, therefore:

M = C*(1.018)^t

Where M is the final amount, C is the initial amount and t is the time elapsed in years. For this case we have:

M = 3800(1.018)^15 = 4965.92626

2. Applying the same line of thought as above, we have:

M = C*(1.04)^t

After 3 years:

M = 2000*(1.04)^3 = 2249.728

After 18 years:

M = 2000*(1.04)^18 = 4051.633

To obtain 3000:

3000 = 2000*(1.04)^t

2000*(1.04)^t = 3000

1.04^t = 3000/2000

1.04^t =1.5

log(1.04^t) = log(1.5)

t*log(1.04) = log(1.5)

t = log(1.5)/log(1.04) = 10.338 years

Answer:

21

Step-by-step explanation:

3/2×14=21

Answer:

21

Step-by-step explanation:

Answer:

A

Step-by-step explanation:

right on Edge.2020

The graph that shows the solution set for -4.4 ≥ 1.6x - 3.6 is A number line going from negative 3 to positive 3. A closed circle is at negative 0.5. Everything to the left of the circle is shaded, the correct option is A.

An Inequality is a statement that is formed when two expressions are joined using an inequality operator.

-4.4 ≥ 1.6x - 3.6

The value of x is

-4.4+3.6 ≥ 1.6x

x ≤ -0.5

The number line of any length, which has a closed circle at -0.5 and the left side of the point -0.5 is shaded is the graph of the inequality.

To know more about Inequality

https://brainly.com/question/20383699

#SPJ5

Given:

Triangle ABC is similar to triangle XYZ.

The measures of the sides are AB = 6 cm, BC = 18 cm and XY = 12 cm

We need to determine the measure of side YZ.

Measure of YZ:

Since, ABC and XYZ are similar triangles, by using similar triangles property, we have;

[tex]\frac{AB}{XY}=\frac{BC}{YZ}[/tex]

Let the length of YZ be x.

Substituting the values, we get;

[tex]\frac{6}{12}=\frac{18}{x}[/tex]

Cross multiplying, we get;

[tex]6x=12 \times 18[/tex]

[tex]6x=216[/tex]

Dividing both sides by 6, we have;

[tex]x=36[/tex]

Thus, the value of x is 36.

Hence, the measure of the side YZ is 36 cm.

Answer:

NOTE: THIS IS AN EXAMPLE

Step-by-step explanation:

Let the Yellow Marbles be “X” and Red Marbles be “Y”

Total is 65, so X+Y = 65

Since we know that Yellow Marbles are 5 more than 4 times red marbles, let us convert that in terms of X and Y as well.

i.e, X = 4Y+5

Now replace X with (4Y+5) in the first equation we wrote above.

(4Y+5)+Y = 65

i.e, 5Y+5 = 65

5Y = (65–5),

5Y = 60

Therefore Y = 60/5 = 12

we know total is 65

So X= 65-Y

X=65–12 = 53

Therefore, the number of Yellow Marbles are 53 and the Red ones are 12.

Answer:

160

Step-by-step explanation:

you need to multiply the ounces of gas by 4 like you did to the oil.

Answer:

160 oz

Step-by-step explanation:

However, I personally think this does not make sense. A leaf blower should take more gas than oil, right? For this reason, I will provide an additional answer.

If the ratio of gas to oil is 40:1, then you would multiply by 4 to get 4 oz oil and 160 oz gas.

Alternate answer:

If the ratio of oil to gas is 40:1, then you divide by 10 on both sides to get 4 oz oil and .1 oz gas.

Alt answer: .1 oz

Answer :

The weight of a sedans in tons is 2.1 tons.

Step-by-step explanation:

Given : Equations [tex]T=s+0.50[/tex] and [tex]T=0.25s+1.70[/tex] where T and s represents the weight in tons of a sedan and of a truck, respectively.

To find : What is the weight of a sedan in tons ?

Solution :

Solving equations,

[tex]T=s+0.50[/tex] ......(1)

[tex]T=0.25s+1.70[/tex]  .....(2)

As LHS is equate we equate RHS,

[tex]s+0.50=0.25s+1.70[/tex]

[tex]s-0.25s=1.70-0.50[/tex]

[tex]0.75s=1.2[/tex]

[tex]s=\frac{1.2}{0.75}[/tex]

[tex]s=1.6[/tex]

Substitute in equation (1),

[tex]T=1.6+0.50[/tex]

[tex]T=2.1[/tex]

Therefore, the weight of a sedans in tons is 2.1 tons.

Answer:

122.293

Step-by-step explanation: