A money box contains only 10-cent and 20-cent coins. There are 40 coins with a total value of $6.50. How many coins of each?

The age of the car that Devon purchased is given by: Option C: 5 years

If the initial amount (also called as principal amount) is P, and the interest rate is R% per unit time, and it is left for T unit of time for that compound interest, then the interest amount earned is given by:

[tex]CI = P(1 +\dfrac{R}{100})^T - P[/tex]

The final amount becomes:

[tex]A = CI + P\\A = P(1 +\dfrac{R}{100})^T[/tex]

We can use compound interest's formula (with a bit modification if necessary) whenever there is compounding on a base amount on some fixed rate for some time.

For this case, there is decrement happening, so rate can be taken negative. Thus, we take:

R = -35%

Let the car is T years old.

Then, as we have: Initial price of the car = P = $16000, and the final price of the car = A = $2000, thus, we get:

[tex]A = P(1 +\dfrac{R}{100})^T\\\\2000 = 16000(1 + (-35/100) )^T\\1/8 = (1-0.35)^T\\0.125 = 0.65^T\\\\T = log_{0.65}(0.125)\\T \approx 4.827 \approx 5 \text{ (in years) }[/tex]

Thus, the age of the car that Devon purchased is given by: Option C: 5 years

Learn more about compound interest here:

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Answer:

C 5 years

Step-by-step explanation:

120 cm^3

The equation for a triangle: 1/2bh.

1/2(a)(b)

1/2(10)(24)

1/2(240)

120 cm^3

Answer:

A

Step-by-step explanation:

the rock lands when it reaches height 0.

so, for what t is h(t) = 0 ?

16t² - 100 = 0

16t² = 100

now we pull the square root on both sides (we can ignore the negative solutions, as negative seconds don't make any sense in our scenario)

4t = 10

t = 10/4 = 5/2 = 2.5 seconds

so, A is correct.

Step-by-step explanation:

By definition, pi is equal to c/d, where c is the circumference and d is the diameter.

This means that C = pi(d).

However, since diameter is twice the radius, if we let the radius be r cm, d=2r.

This gives that C=2pi(r).

Step-by-step explanation:

what do you mean by "the hard part" ?

anyway,

we need to sum the numbers in every column creating 5 sums.

then we need to multiply these 5 numbers (product) and divide the result by 16 (we need 1/16 of that product).

so, we have

5 + 1 = 6

1 + 6 + 4 + 8 = 19

2 + 1 + 3 = 6

2 + 5 = 7

1 + 0 + 7 = 8

6×19×6×7×8 = 38,304

38,304 / 16 = 2394

that is your code : 2394

Answer:

  50 cm²

Step-by-step explanation:

Given that the regular polygon is a square, there are multiple ways you can jump directly to the answer. Perhaps the simplest is to use the formula for the area of a rhombus:

  A = 1/2(d1)(d2)

where d1 and d2 are the lengths of the diagonals. Here, we see that half the diagonal is 5 cm, so the area is ...

  A = (1/2)(10 cm)(10 cm) = 50 cm² . . . . area of the polygon

__

Alternate solution

If you want to use the radius and the number of sides in a formula, you can consider the area of each triangle formed by radii and a side. That triangle has area ...

  A = 1/2r²sin(α)

where r is the radius and α is the central angle. For an n-sided polygon, the area is the sum of n of these triangles, and the central angle is 360°/n. Then the polygon area is ...

  A = n/2·r²·sin(360°/n)

For n = 4 and r = 5 cm, the area is ...

  A = (4/2)(5 cm)²(sin(360°/4)) = 2(5 cm)²(1) = 50 cm² . . . . area of square

_____

Additional comment

The formula is somewhat different if you start with the length of the apothem. One way to find the area is using the above formula and the relation between the radius and apothem:

  r = a·sec(180°/n)

Another formula uses the apothem directly:

  A = n·a²·tan(180°/n)

Answer:

Bc 23

Step-by-step explanation:

because you muply 42 to 65 and u will get that the same answer

Answer:

-9 < x < 9

Step-by-step explanation: "<" is the symbol for "less than". -9 is less than x, or x is greater than -9. x is less than 9.

Check the picture below.

With the given budget, the inequality that must be used is:

$5.5*s ≤ $350

We know that the budget is $500.

Then, we know that there is a fixed cost of $150, then the budget left is:

$500 - $150 = $350

With these $350 they pay the food for the students, which costs $5.50 per student.

So the number of students that can go must be such that:

s*$5.50 ≤ $350

There says that the cost in food for the s students must be smaller than or equal to the remaining $350.

So the correct option is the second one.

If you want to learn more about inequalities, you can read:

https://brainly.com/question/18881247

Answer:

s^2 = 324 would mean side length s = 18

Step-by-step explanation:

The square root of 324 would be 18.

A square with side length s has an area of 324 square centimeters. So, the side of the square is 18cm

The area of a square can be calculated as the square of the sides of a given figure.

The area of a square = [tex]side^2[/tex]

A square with side length s has an area of 324 square centimeters.

The area of a square = [tex]side^2[/tex]

then s = √324

           =18

Thus, the side of the square is 18cm

Learn more about the area;

https://brainly.com/question/11952845

Answer:

270 Miles

Step-by-step explanation:

18 miles per gallon

15 gallons

Basically count 18, 15 times

18*15=270

The van can travel 270 miles

Step-by-step explanation:

(2,4)===(4,-2)

(4,3)===(3,-4)

(2,3)===(3,-2)

Answer:

I believe the answers are a and e.

Step-by-step explanation:

Let me know if you want an explanation.

Hope this helps!!!

Answer:

9

Step-by-step explanation:

5% of 180 = 5/100 x 180

=> 5/10 x 18

=> 90/10

=> 9

Answer:

9

Step-by-step explanation:

5% of 180 = 5/100 of 180

10% = 18 ----->  5% = 9

180 = ?/1000 ------->  180 = 18000 / 100    =  180

5% of 180 = 9

Answer:

No, no, no, yes, yes.

Step-by-step explanation:

A integer is a whole number, 1, 2, 3, etc.

Answer:

x = 8

Step-by-step explanation:

Answer:

x = 8

m∠M = 52°

m∠K = 52°

m∠L = 128°

m∠J = 128°

Step-by-step explanation:

If the given shape is a parallelogram, its opposite interior angles are equal.

⇒ m∠M = m∠K

⇒ 7x - 4 = 5x + 12

Subtract 5x from both sides:

⇒ 2x - 4 = 12

Add 4 to both sides:

⇒ 2x = 16

Divide both sides by 2:

⇒ x = 8

Substitute found value of x into the expressions for each angle to find the measures of the angles:

⇒ m∠M = 7(8) - 4 = 52°

⇒ m∠K = 5(8) + 12 = 52°

As the angles on the same side of the transversal in a parallelogram sum to 180°, then

⇒ m∠J + m∠M = 180°

⇒ m∠J = 180° - m∠M

⇒ m∠J = 180° - 52°

⇒ m∠J = 128°

As m∠L = m∠J  then m∠L = 128°

Check the picture below.  When will it reach its height? well, at the vertex, so

[tex]~~~~~~\textit{initial velocity in feet} \\\\ h(t) = -16t^2+v_ot+h_o \quad \begin{cases} v_o=\textit{initial velocity}&24\\ \qquad \textit{of the object}\\ h_o=\textit{initial height}&50\\ \qquad \textit{of the object}\\ h=\textit{object's height}\\ \qquad \textit{at "t" seconds} \end{cases} \\\\\\ h(t)=-16t^2+24t+50\implies \\\\[-0.35em] ~\dotfill\\\\ \textit{vertex of a vertical parabola, using coefficients}[/tex]

[tex]h(t)=\stackrel{\stackrel{a}{\downarrow }}{-16}t^2\stackrel{\stackrel{b}{\downarrow }}{+24}t\stackrel{\stackrel{c}{\downarrow }}{+50} \qquad \qquad \left(-\cfrac{ b}{2 a}~~~~ ,~~~~ c-\cfrac{ b^2}{4 a}\right) \\\\\\ \left(-\cfrac{ 24}{2(-16)}~~~~ ,~~~~ 50-\cfrac{ (24)^2}{4(-16)}\right)\implies \left( \cfrac{3}{4}~~,~~50-\cfrac{576}{64} \right)[/tex]

[tex]\left(\cfrac{3}{4}~~,~~50+9 \right)\implies \stackrel{\underset{\qquad \downarrow }{\textit{how far up it went}}}{\underset{\stackrel{\uparrow \qquad ~~}{\textit{when it reached it}}}{\left( \cfrac{3}{4}~~,~~59 \right)}}[/tex]

Answer: 12 units

Step-by-step explanation:

If you graph them on a graph you count the units between them and that is your anwser.

Answer:

12 units

Step-by-step explanation:

calculate DG using the distance formula

d = [tex]\sqrt{(x_{2}-x_{1})^2+(y_{2 -y_{1} } )^2[/tex]

with (x₁, y₁ ) = D (8, 3 ) and (x₂, y₂ ) = G (- 4, 3 )

DG = [tex]\sqrt{(-4-8)^2+(3-3))^2}[/tex]

     = [tex]\sqrt{(-12)^2+0^2}[/tex]

     = [tex]\sqrt{144+0}[/tex]

    = [tex]\sqrt{144}[/tex]

    = 12

Answer:

X= 5/18

Step-by-step explanation:

Answer:

Step-by-step explanation:

c

so you have to combine like terms so subtract 8 - 4 and the 4 disappears so it be like this

8 - 2x = 4 + x

-4 -2x = -4 + x

4 - 2x = x

next combine the like terms of the 2x so

4 - 2x = x

4 + 2x = +2x

4 = 2x

now you divide 4 by 2 so like this

4 = 2x

2   2

and your answer is x = 2 try to solve the other one if you need help ask me

Answer:  3a - 2b + 3

Step-by-step explanation:

(3a + 2b - 7) - (4b - 10)

open the bracket

3a + 2b - 7 - 4b + 10

combine like terms

3a + 2b - 4b - 7 + 10

3a - 2b + 3

Answer:

Step-by-step explanation:

Y=(X-3) 3+1

1. Flip the way the equation is facing

1+3 (3-x)=Y

2. Add or Subtract

4 (3-x)=Y

3. Do the parentheses

4(-3x)=Y

4. Solve for X ( Undo addition or Subtraction)

(4-4)=0

What ever you do to one side you have to do to the other!

Y-4

Your New Equation Looks Like

-3x= -4 + Y

5. Undo Multiplication

-3x/3= x

What ever you do to one side you have to do to the other!

-4/3 y/3

6. Divide Y

y/3= 3

7. New equation

X= -4/3 + 3

8. Plug in X to the Original Equation

Y=2(-4/3+3) -3 +(3+1)

9. Solve accordingly

Answer:

he correct answer is D. 12 adult tickets, 4 child ticket

Step-by-step explanation:

Answer: n = 3

Step-by-step explanation:

divide 3.5n by 3.5n then divide 10.5 by 3.5 which is

n = 3

Answer:

[tex]\boxed{\sf{n=3}}[/tex]

Step-by-step explanation:

To find the value of n, you have to isolate it on one side of the equation.

3.5n=10.5

First, multiply by 10 from both sides.

[tex]\sf{3.5n*10=10.5*10}[/tex]

Solve.

35n=105

Divide by 35 from both sides.

35n/35=105/35

Solve.

105/35=3

n=3

I hope this helps you! Let me know if my answer is wrong or not.