10 fish are swimming in the ocean, 6 of them drown, how many are left?

The explicit formula is [tex]a_{n-1} = 256 * 0.5^{n-1[/tex] and the sum of the first 25 terms is approximately 512

The given parameters are:

[tex]a_0 = 256[/tex]

[tex]a_{n +1} = 0.5a_n[/tex]

Set n = 0

[tex]a_1 = 0.5a_0[/tex]

Substitute 256 for a0

[tex]a_1 = 0.5 * 256[/tex]

[tex]a_1 = 128[/tex]

This means that the common ratio is 0.5.

The explicit formula is then represented as:

[tex]a_{n-1} = a_0 * r^{n-1[/tex]

This gives

[tex]a_{n-1} = 256 * 0.5^{n-1[/tex]

This is calculated using:

[tex]S_n = \frac{a_0(r^{n-1} -1)}{r - 1}[/tex]

This gives

[tex]S_{25} = \frac{256 * (0.5^{25-1} -1)}{0.5 - 1}[/tex]

Evaluate

[tex]S_{25} = 512[/tex]

Hence, the sum of the first 25 terms is approximately 512

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Work Shown:

12x+10

2*6x+2*5

2(6x+5)

Effectively, we use the distributive property in reverse when it comes to factoring expressions like this.

The distributive property in general is a*(b+c) = a*b+a*c

1) Find the Greatest Common Factor (GCF).

1 What is the largest number that divides evenly into 12 and 10?

It is 2.

2 What is the highest degree of  that divides evenly into 12and 10?

It is 1, since x is not in every term.

3 Multiplying the results above,

The GCF is 22.

2) Factor out the GCF. (Write the GCF first. Then, in parentheses, divide each term by the GCF.)

[tex]2(\frac{12x}{2}+\frac{10}{2})[/tex]

3) Simplify each term in parentheses.

2(6x+5)

Answer:

[tex]3\ln 4 + 3 \ln a[/tex]

Step-by-step explanation:

[tex]\ln(4a)^3\\\\=3\ln (4a)~~~~~~~~~~~~~~~~~~~~~~~~~~~~;[\log_b m^n = n \log_b m]\\\\=3(\ln 4 + \ln a)~~~~~~~~~~~~~~~~~~~~;[\log_b (mn) = \log_b m + \log_b n]\\\\=3\ln 4 + 3 \ln a[/tex]

The option (A) "The graph of function f is shifted right 3 units and up 4 units. " is correct.

It is defined as a special type of relationship, and they have a predefined domain and range according to the function every value in the domain is related to exactly one value in the range.

We have a transformation function:

g(x) = f(x - 3) + 4

The parent function is f(x).

First transformation:

x → (x - 3)

The function will shift right by 3 units.

Second transformation:

Add 4 to the function:

g(x) = f(x - 3) + 4

The function will shift up by 4 units.

Thus, the option (A) "The graph of function f is shifted right 3 units and up 4 units. " is correct.

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I think it's 28 units²

Answer:

it is b.

Step-by-step explanation:

as if the slope of x is 5 then y,=,0

The perimeter of the triangle is 16 feet

The perimeter of a triangle refers to the calculation of the total distance bounded by the triangle or around the triangle.

Perimeter of a triangle = (3x - 4) + (x² - 1) + (2x - 15)

Perimeter of a triangle = 5x + x² - 20

Perimeter of a triangle =  5(4) + (4)² - 20

Perimeter of a triangle = 16

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Answer:

[tex]x > \frac{5}{2} > 2\frac{1}{2}[/tex]

Step-by-step explanation:

group

[tex]4x-7 > 3\\4x-7+7 > 3+7\\4x > 3+7\\4x > 10[/tex]

isolate "x"

[tex]4x > 10\\=\frac{4x}{4} > \frac{10}{4}\\x > \frac{10}{4}\\x > \left(\frac{5\cdot 2}{2\cdot 2}\right)\\x > \frac{5}{2}[/tex]

Answer:

x > 2.5 or in fraction form x > 2 1/2

Step-by-step explanation:

4x - 7 > 3

     +7  +7         Add seven to both sides.

4x > 10

÷4     ÷4            Divide both sides by 4.

x > 2.5

Hope this helps!

The cash value of the computer system in 3 years will be $1632. The correct option is the third option $1632

From the question, we are to determine the cash value of the computer system in 3 years

From the given information,

The computer system cost $2,395 and it will depreciate at a rate of 12% a year

After the first year, the worth of the computer system will be

$2,395 - (12% of $2,395)

$2,395 - (0.12 × $2,395)

= $2,395 - $287.4

= $2107.6

After the second year, the worth of the computer system will be

$2107.6 - (12% of $2107.6)

$2107.6 - (0.12 × $2107.6)

= $2107.6 - $252.912

= $1854.688

After the third year, the worth of the computer system will be

$1854.688 - (12% of $1854.688)

$1854.688 - (0.12 × $1854.688)

= $1854.688 - $222.56256

= $1632.12544

≅ $1632

Hence, the cash value of the computer system in 3 years will be $1632. The correct option is the third option $1632

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At the equilibrium price p, we can solve for the quantity of goods x :

demand = supply

5200 - 0.0005x = 2800 + 0.0003x

2400 = 0.0008x

x = 3,000,000

With this quantity of goods, the equilibrium price is

p = 5200 - 0.0005 (3,000,000)

p = 5200 - 1500

p = 3700

Answer:

6

Step-by-step explanation:

The constant is the number that's all by itself with no variable.

x is the variable. It can vary (change) as you use different values for x.

There are four terms here in the expression in your question they are separated by the plus or minus signs.

2 and 4 are exponents. 3 and 5 are coefficients.

x^4 is a fourth degree term. 3x^2 is a second degree term. 5x is a first degree term. The whole expression is 4th degree because the highest exponent is 4.

But the 6 is all by itself. 6 is the constant.

Answer:

  C.  g(x) = 3·2^x +2

Step-by-step explanation:

The graph of g(x) appears to be a translation upward of the graph of f(x).

__

To find the equation of g(x), we can add 5 to f(x), since the translation appears to be 5 units. (The y-intercept of f(x) is 0; the y-intercept of g(x) is 5.)

  g(x) = f(x) +5

  g(x) = (3·2^x -3) +5

  g(x) = 3·2^x +2

__

You can also determine the correct choice by looking at the value at x=0:

  A. g(0) = 3 +6 = 9

  B. g(0) = 1 +3 = 4

 C. g(0) = 3 +2 = 5 . . . . matches g(0) on the given graph

  D. g(0) = 3

The value of x from the figures are 18 and 26 respectively

13) From the diagram, the angles at the corner is 90 degrees. This shows that the sum of the angles is complementary (sum is 90 degrees)

3x + 2x = 90

5x = 90

x = 90/5

x = 18

15) Since the sum of angles on a straight line is supplementary, hence;

6x + x - 2 = 180

7x = 182

x = 182/7

x = 26

Hence the value of x from the figures are 18 and 26 respectively

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Answer:

there's no picture dude

How much is $100 in ZA rands.

Let the unknown be "x"

[tex]\frac{1}{17}×\frac{100}{x}[/tex]

We'll have to do cross multiplication.

So we'll have to multiply 100 and 17.

[tex]100×17[/tex]

[tex]\huge\boxed{= 1700 \: ZA \: rands}[/tex]

Therefore, $100 is 1700 ZA rands.

Answer:

i think you have to multiply

Step-by-step explanation:

Answer:

30

Step-by-step explanation:

The formula for the perimeter of a rectangle is, P = length + breadth + length + breadth.

so, P = 9+6+9+6

P = 30

The product of the complex numbers 65(cos(14°)+ i sin(14°)) and 8(cos(4°)+ i sin(4°)) is 520[cos(18) + isin(18)]

An equation is an expression that shows the relationship between two or more numbers and variables.

Complex number is in the form z = a + bi, where a and b are real numbers.

The product of the complex numbers 65(cos(14°)+ i sin(14°)) and 8(cos(4°)+ i sin(4°)) is:

z = 65 * 8 [cos(14 + 4) + isin(14 + 4)] = 520[cos(18) + isin(18)]

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Answer: The answer is 22

Step-by-step explanation: you divide the 36 and the 9 to get 4 then you add the 18 and the 4 to get 22

Answer:

22

Step-by-step explanation:

[tex]18+(\frac{36}{9})=?\\ 18+4=?\\22=?[/tex]

0.75 + 1.25 = $2 everyday

Since there are 5 weekdays:

5 x 2 = $10 a week

Since there are 52 weeks in a year:

10 x 52 = $520 a year!

Answer:

i don't know, you need to tell us what we need to do

Step-by-step explanation:

Answer:

-16.

Step-by-step explanation:

2/3 * (-3) * (4*5 + 6 - 2(-3)^2)

= -2(20 + 6 - 18)

= -2 * 8

= -16.

Answer:

51%

Step-by-step explanation:

Answer:

Step-by-step explanation:

The value of z is 7 when y = 7 and x = 14.

If x varies directly as y and inversely as z and when y = 16 and z = 14,  x = 16. Enter the value of z when y = 7 and x = 14.

The variation involves a direct and inverse variation from x to y and z.

This is represented as:

[tex]x = \frac{ky}{z}[/tex]

Where k is the constant of variation

For the first set of values, we have:

[tex]16 = \frac{k * 16}{14}[/tex]

Solve for k

k = 14

For the second set of values, we have:

[tex]14 = \frac{k * 7}{z}[/tex]

Substitute 14 for k

[tex]14 = \frac{14 * 7}{z}[/tex]

Solve for z

z = 7

Hence, the value of z is 7

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Step-by-step explanation:

Here in the given figure the value of x will be 70° ( being alternative angle )

x = 70°

Now...

y = 60° ( being corresponding angle )

Now...

60° + 70° + z = 180° ( the sum of interior angle of triangle is 180°

z = 180° - 130°

z = 50° ..

[tex]...[/tex]

The value of x and y in the right angle triangle are 6 units and 10.4 units.

The sides of a right triangle can be found as follows:

using trigonometric ratio,

sin 60 = opposite / hypotenuse

sin 60 = y / 12

cross multiply

y = 12 sin 60

y = 10.3923048454

y = 10.4 units

Therefore,

cos 60 = adjacent / hypotenuse

cos 60 = x / 12

x = 12 cos 60

x = 6 units

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So we conclude that x measures 6 units and y measures 10.39 units.

Here we have a right triangle.

x is the adjacent cathetus to the shown angle, and y is the opposite cathetus. We can see that the hypotenuse measures 12.

Then using trigonometric relations we get:

So we conclude that x measures 6 units and y measures 10.39 units.

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Answer:

i) 0.5

ii) 0.76

Step-by-step explanation:

i) 0.5

ii) 0.76