At the beginning of year 1, Matilda invests $450 at an annual simple interest rate of 5%. She makes no deposits to or withdrawals from the account. Which explicit formula can be used to find the account's balance at the beginning of year 15? What is the balance?

Answer:

6 x 0,30 = $1,80

$3,30 - $1,80 = $1,50

$1,50 - $1,25 = $0,25 (not enough money)

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[tex]\begin{array}{ccll} Lbs&\$\\ \cline{1-2} 1&2.99\\ 3.2&x \end{array}\implies \cfrac{1}{3.2}=\cfrac{2.99}{x}\implies x = (3.2)(2.99)\implies \stackrel{\textit{rounded up}}{x = 9.57}[/tex]

Given:

The given function is:

[tex]f_1(x)=-3\cdot 2^{x-5}-4[/tex]

The graph of the function is given.

To find:

The end behavior of the given function.

Solution:

We have,

[tex]f_1(x)=-3\cdot 2^{x-5}-4[/tex]

From the given graph it is clear that the function approaches to -4 at x approaches negative infinite and the function approaches to negative infinite at x approaches infinite.

[tex]f_1(x)\to -4[/tex] as [tex]x\to -\infty[/tex]

[tex]f_1(x)\to -\infty[/tex] as [tex]x\to \infty[/tex]

Therefore, the end behaviors of the given function are:

[tex]f_1(x)\to -4[/tex] as [tex]x\to -\infty[/tex]

[tex]f_1(x)\to -\infty[/tex] as [tex]x\to \infty[/tex]

Answer:

volume of the sphere=4/3πr³

=4/3×3×1³ inch³

=4 inch³

D. 11520m

Answer:

Solution given:

initial velocity[u]=480m/s

g=10m/s²

maximum height=?

now

we have

maximum height=[tex]\frac{u²sin²\theta}{2g}[/tex]

where

[tex]\theta=90°[/tex]

=[tex]\frac{480²*sin90}{2*10}=11520m[/tex]

Answer:

(1/3) r2 =(1/3) r +14

1/6 divided by 83 r + 14

97r

i think...

I hope this helps you!

XoXo Mashayla

Step-by-step explanation:

Answer:

The short pieces are 10  cm each and the long pieces are 15 cm each.

Step-by-step explanation:

We cut a 60cm rope into 5 pieces. There are 3 short pieces that measure the same and the other 2 pieces are 5cm longer than the short ones. How long are the pieces?

let the length of the short pieces is p.

Length of longer pieces = p + 5

So,

60 = 3 p + 2 (p+ 5)

60 = 3 p + 2p + 10

5 p =  50

p = 10 cm

So, the short pieces are 10  cm each and the long pieces are 15 cm each.

Answer:

A. 4x² + 9x/4 - 7

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Algebra I

Step-by-step explanation:

Step 1: Define

Identify

f(x) = x/4 - 3

g(x) = 4x² + 2x - 4

(f + g)(x) is f(x) + g(x)

Step 2: Find

Answer:

A

Step-by-step explanation:

Answer:

B

Step-by-step explanation:

Total waste = 22 000 in^3

If we use a proportion we have:

x : 100 = 2000 : 22 000

x = 200 000 / 22 000 = 9,09 % (option a is wrong

x : 100 = 7000 : 22 000

x = 700 000 / 22 000 = 31 % (ok)

Answer:

the answer is B

Step-by-step explanation:

-5(y-2)-7y

-5y-10-7y

+7y +7y

answer: 2y-10

Answer:

A. (-12y+10)

Step-by-step explanation:

-5(y-2) - 7y can be simplified to:

-5y + 10 - 7y when you factor the parenthesis.

If you add the y's together, the answer should be:

-12y + 10.

.

Answer:

2 cases of soya bean milk will have the same volume as 1 case of fruit juice.

Step-by-step explanation:

Let the case of soya beans drink be x and let the case of fruit juice be y

We are told that the room can store either 10 cases of soya beans drink and 8 cases of fruit juice or 4 cases of soybeans drink and 11 cases of fruit juice.

This means that;

10x + 8y = 4x + 11y

Rearranging, we have;

10x - 4x = 11y - 8y

6x = 3y

Thus;

y = 6x/3

y = 2x

This means that 2 cases of soya bean milk will have the same volume as 1 case of fruit juice.

Answer:

Step-by-step explanation:

Cube with side 2 has volume:

Cube with side 6 has volume:

Number of cubes:

option A.55°

Answer:

Solution given:

<x+<y=<z

exterior angle of a triangle is equal to the sum of two opposite interior angle

4n-18+n+8=133-6n

5n+6n=133+10

11n=143

n=143/11

n=13

exterior angle =133-6*13=55°

option A.55°

Answer:

y = 13/3

Step-by-step explanation:

substitute y=2x+5 in x+y = 4

x+2x+5 = 4

3x+5=4

3x= -1

x= -1/3

substitute x= 1-/3 in x+y = 4

-1/3 +y = 4

y = 13/3

Answer:

less than, less than, greater than (from top to bottom)

Step-by-step explanation:

Answer:

Step-by-step explanation:

Answer:5/4

Step-by-step explanation: i think this is the answer

Answer:

The area is 30 units squared, the perimeter is 17 units, and the answer to the question below is 9

Step-by-step explanation:

Answer:

  x,y = -4, -15

Step-by-step explanation:

Answer:

-2.179

Step-by-step explanation:

Given :

Degree of freedom, df = 12

Area to the left = 0.025

The value of T can be obtained using either a t distribution table or a T value calculator :

t0.025, 12 (to the left) = t(1-0.025), 12 = t0.975,12 = - 2.1788

Therefor le, t value with 12 degree of freedom, with area to the left being 0.025 is - 2.179

The red line is perpendicular to the y-axis.

Answer:

Given: DB = 7.2 cm, AE = 1.8 cm and EC = 5.4 cm and DE || BC.

DB

AD

=

AC

AE

[by basic proportionality theorem which states that if a line is drawn parallel to one side of a triangle the other two sides in distinct points, then the other two sides are divided in the same.

7.2

AD

=

5.4

1.8

AD=

5.4

7.2×1.8

AD=

10

24

⟹AD=2.4cm

First, we need to draw a right triangle to represent the given trigonometric ratio. (Kindly refer to the attached photo for the figure.)

Second, we need to determine the length of the unknown side.

In this case, the unknown side is the hypotenuse. Since the length of the opposite side is 12 and the length of the adjacent side is 16, then the length of the hypotenuse is

[tex]c = \sqrt{16^{2} + 12^{2}}[/tex]

[tex]c = 20[/tex]

After this, we need to know the trigonometric identity of sin 2A in order to solve for its value.

We know that,

sin 2A = 2 sin A cos A

Then, we need to determine the values of sin A and cos A.

Based on the figure (attached photo), the values of sin A and cos A are

sin A = opposite side / hypotenuse

sin A = 12/20

sin A = 3/5

cos A = adjacent side / hypotenuse

cos A = 16/20

cos A = 4/5

Finally, we can now solve for the value of sin 2A by substituting the values of sin A and cos A to the trigonometric identity of sin 2A.

Therefore, the the value of sin 2A is

sin 2A = 2 sin A cos A

sin 2A = 2(3/5)(4/5)

sin 2A = 24/25

Answer:

5 in

Step-by-step explanation:

by doing a proportion of 2/4 for the known sides, you can find that the smaller triangle has sides that are half of the larger one. so 10/2 equals 5

Answer: X = 5

Step-by-step explanation:

4 divided by 2 = 2

So 10 divided by 2 = 5

Answer:

[tex] \displaystyle 4320 {x }^{3} [/tex]

Step-by-step explanation:

to solve binomials like this there's a way called binomial theorem given by

[tex] \displaystyle {(a + b)}^{n} = \sum _{k = 0} ^{n} \binom{n}{k} {a}^{n - k} {b}^{k} [/tex]

but for this question we need the following part

[tex] \displaystyle \boxed{ \binom{n}{k} {a}^{n - k} {b}^{k} }[/tex]

from the question we obtain that a,b and n is 3x,4 and 5 since we want to find the coefficient x³ k should be (5-3) = 2 so we have determined the variables now just substitute

[tex] \displaystyle \binom{5}{2} {(3x)}^{5 - 2} \cdot {4}^{2} [/tex]

simplify which yields:

[tex] \displaystyle \boxed{ \bold{4320 {x }^{3}} }[/tex]

and we are done!

Answer:

No. Try harder next year.

Answer:

Systematic Sampling

Step-by-step explanation:

According to the Question,

So, systematic sampling is right Answer.

Answer:

Systematic Sampling

Step-by-step explanation:

What type of sampling did the daycare operator use Systematic Sampling.

Answer:

sum of three positive integer=57

Step-by-step explanation:

let x,y,z be three positive no.

given :-

xyz=7³

xyz=343

xyz=1×7×49

x+y+z=(1+7+49)

sum=57

Answer:

343

Step-by-step explanation:

7^3

change 7^3 to a natural number or enter 7^3 on a calculator

7×7×7

=343

factors of 343=1,7,49,343

1×7×49=343

1+7+49=57

Answer:

To subtract integers, change the sign on the integer that is to be subtracted. If both signs are positive, the answer will be positive. If both signs are negative, the answer will be negative. If the signs are different subtract the smaller absolute value from the larger absolute value