20 points and brainly ;) You earned $1600 in interest in your savings account over 10 years at a rate of 8%. How much money did you originally deposit into your savings account?

Answer:

[tex]a_n = (\frac{1}{4})2^{n-1}[/tex]

Step-by-step explanation:

Geometric sequence:

In a geometric sequence, the quotient between consecutive terms is the same, and this quotient is given by q.

The explicit rule of a geometric sequence is given by:

[tex]a_n = a_1q^{n-1}[/tex]

In which [tex]a_1[/tex] is the first term.

1/4, 1/2, 1, 2, 4

This means that [tex]a_1 = \frac{1}{4}[/tex], and:

[tex]q = \frac{4}{2} = \frac{2}{1} = \frac{1}{\frac{1}{2}} = \frac{\frac{1}{2}}{\frac{1}{4}} = 2[/tex]

So the explicit rule is:

[tex]a_n = (\frac{1}{4})2^{n-1}[/tex]

Answer:

I think iit's no consistent

Step-by-step explanation:

no consistent because there is no multiplying happening and no consistent adding happening

Answer:

x=0

Step-by-step explanation:

3x + 10 = 10 + 2x

Subtract 2x from each side

3x-2x + 10 = 10 + 2x-2x

x+10 = 10

Subtract 10 from each side

x+10-10 = 10-10

x=0

Answer:

x=0

Step-by-step explanation:

3x + 10 = 10 + 2x

Subtract 2x from each side

3x-2x + 10 = 10 + 2x-2x

x+10 = 10

Subtract 10 from each side

x+10-10 = 10-10

x=0

Answer:

Let x represent the number of sales each man had.

For Salesman A, he earns $65 per sale; this is 65x.

For Salesman B, he earns $40 per sale; this is 40x.  We also add to this his weekly salary of $300; this gives us 40x+300.

Since their pay was equal, set the two expressions equal

Step-by-step explanation:

65x = 40x+300

Subtract 40x from each side:

65x-40x = 40x+300-40x

25x = 300

Divide both sides by 25:

25x/25 = 300/25

x = 12

Step-by-step explanation:

2C – 3B = 2(1+5n-6n²)-3(n+4n²)

= 2+10n-12n²-3n-12n²

= 2 +7n -24n²

The expression (2C-3B) equals to (-24x²+7x+2)

Expressions in maths are mathematical statements that have a minimum of two terms containing numbers or variables, or both, connected by an operator in between.

Given are two expression, C = 1+5n-6n² and B = n+4n²

2C = 2+10n-12n²

3B = 3n+12n²

2C-3B = 2+10n-12n² - 3n-12n²

= -24n²+7n+2

Hence, The expression (2C-3B) equals to (-24x²+7x+2)

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Answer:

[tex] \frac{6}{6 - 2} = \frac{6}{4} = \frac{3}{2} [/tex]

Answer:

[tex] \rm \rightharpoonup \: f(x) = \frac{x}{x - 2} \\ \rm \rightharpoonup \: f(6) = \frac{6}{6 - 2} \\ \rm \rightharpoonup \: \frac{6}{4} \\ \rm \rightharpoonup \: \frac{3}{2} [/tex]

Answer:

B (8x7)-23 is the answer

Subtracting 23 from the product of 8 and 7 can be written as (8 X 7) - 23 option (B) is correct.

It is defined as the operation in which we do the addition of numbers, subtraction, multiplication, and division. It has a basic four operators that is +, -, ×, and ÷.

We have:

Subtract 23 from the product of 8 and 7

The product of the 8 and 7 can be written as (8 X 7)

Subtract 23 from (8×7)

(8 X 7) - 23

Thus, subtracting 23 from the product of 8 and 7 can be written as (8 X 7) - 23 option (B) is correct.

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Answer:

He showed that f(n) ÷ f(n - 1) was a constant ratio.

Given that Jake has proved that a function f(x) is a geometric sequence.

GEOMETRIC SEQUENCE:  A geometric sequence is a sequence of numbers where each term is found by multiplying the preceding term by a constant called the common ratio, r.

So, in Jame's proof, he showed that each term is multiplied by a constant to get the next term.

That is, if 'c' is the constant that was used in the proof, then we must have

This implies that

Therefore, he showed that  f(n) ÷ f(n - 1) was a constant ratio.

Step-by-step explanation:

solution given.

relationship between perpendicular and base is given by tan angle

tan ø=perpendicular/base

ø=tan-¹(4/13)=17.10272897=17° is your answer

Answer:

100000

Step-by-step explanation:

First multiplt the given njmber with 2000 and subrat total number givem

Answer: c

Step-by-step explanation:

Answer:

1/12

Step-by-step explanation:

Given the following :

Actual height of pyramid = 24 ft

Dimension of scaled model :

Height = 2ft ; width = 1ft

a scale factor is a number used to reproduce a reduced dimension of a model by multiplying the actual dimeznsion or size of the model or object.

Since the height is of the scaled model is less than the actual height of the pyramid ; then it could be said that the scale factor is a fraction, because reduction has occurred.

(Height of scaled model / height of actual pyramid)

(2ft / 24ft) = 1/12

Answer: Step-by-step explanation:

List of prime numbers before 41 (including 41 itself): 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41.

Step-by-step explanation:

X+3X+90=360

4X+90=360

4X=360-90

4X=270

270÷4=67.5

X=67.5 degrees

Answer:

V = 168 km³

Step-by-step explanation:

We are given a triangle prism.

Volume of a triangle prism = ½*a*c*h

Where,

a = 8 km

c = 6 km

h = 7 km

Substitute

V = ½*8*6*7

V = 4*6*7

V = 168 km³

Answer:

Radius, r = 2.80 cm

Step-by-step explanation:

Given the following data;

Volume of cylinder = 207 cm³

Height = 8.4 cm

Pie, π = 3.14

To find the radius of the water bottle;

Mathematically, the volume of a cylinder is given by the formula;

V = πr²h

Where;

V is the volume of a cylinder.

r represents the radius of the cylinder.

h represents the height of the cylinder.

Substituting into the formula, we have;

207 = 3.14 * r² * 8.4

207 = 26.376r²

r² = 207/26.376

r² = 7.85

r = √7.85

Radius, r = 2.80 cm

Answer:

2 and 3  

Step-by-step explanation:

2) If two polygons are similar, the ratio of their areas is equal to the square of the ratio of their corresponding sides. 

side ratio:  1/4-------   area ratio: 1²/4²  =  1/16   = 1:16 ratio

3)If two polygons are similar, then the ratio of their perimeters is equal to the ratios of their corresponding side lengths.

The ratio of the perimeters is the same as the scale factor.

 scale 1:4

Answer:

2.5 cm

Step-by-step explanation:

6*5=30

30/2=15

That's the area of the triangle

The area of the rectangle must also equal 15

6*w=15

Divide by both sides by 6

This gives you: 2.5

The value of the width of rectangle w for which the triangle and the rectangle have the same area is, 2.5 cm

Used the formula of area of the rectangle and area of the triangle which states that,

Area of rectangle = Length × Width

And, Area of triangle = 1/2 × Base × Height

Given that,

The triangle and the rectangle have the same area.

Here, in a triangle;

Base = 5 cm

Height = 6 cm

So, the Area of the triangle is,

[tex]A = \dfrac{1}{2} \times 5 \times 6[/tex]

[tex]A = 15 \text{ square cm}[/tex]

In a rectangle;

Length = 6 cm

Width = w cm

So, the area of a rectangle,

[tex]A = 6 \times w[/tex] [tex]\text{ square cm}[/tex]

Since the triangle and the rectangle have the same area.

So, equate both the area of the triangle and rectangle,

[tex]6 \times w = 15[/tex]

Divide both sides by 6,

[tex]w = \dfrac{15}{6}[/tex]

[tex]w = 2.5 \text{ cm}[/tex]

So, the value of w is 2.5 cm

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Answer:

D. 125cm

Step-by-step explanation:

Round each number for an estimate so you get 5 x 5 x 5 = 125

Answer:

5'9 ft

Step-by-step explanation:

He was built different

Answer:

27.7"

Step-by-step explanation:

use the pythagorean theorem

a² + b² = c²

a² + 16² = 32²

a² + 256 = 1,024

subtract 256 from both sides

a² = 768

Take the square root of both sides

a = 27.7128129211

a = 27.7"

Answer:

308 (Third Option)

Step-by-step explanation:

Have a Great Day! :D

Answer:

Y = 0.09X1 - 167.40

Step-by-step explanation:

Year (X) : 2000, 2004, 2006, 2007, 20008

Population (millions) (Y) : 7.08, 7.48, 7.64, 7.71, 7.77

Using technology, the regression model obtained is :

Y = 0.09X1 - 167.40

With a slope of 0.09 and intercept of - 167.40

Answer:

900 cm

Step-by-step explanation:

Proportions

1cm  ⇒ 50cm

18cm ⇒ Wcm

W = 18*50/1

W = 900cm

Step-by-step explanation:

X=63 and Y=27 is the correct answer.