A sequence is defined recursively using the formula f(n+1) =-0.5f(n) . If the first term of the sequence is 120, what is f(5)?

−15
−7.5
7.5
15

Ratio means the quantitative relation between two amounts showing the number of times one value contains or contained in order

example 4 and 6

for example

if we have 4 men and 6 women

we can say the ratio of men to women is 4 to 6

that is 4 : 6

and ratio can also means division

for 4 and 6

= 4 / 6

= 2 / 3

= 2 : 3

that is, for every 2 men we have 3 women

The absolute value inequality is given by | x-130745 | > 10000

and the possibility of Car B is  x < 120745  or  x > 140745

What is absolute value inequality?

Absolute value inequality are inequalities in algebra that involve algebraic expressions with absolute value symbols and inequality symbols. In simple words, we can say that an absolute value inequality is an inequality with an absolute value symbol in it. It can be solved using two methods of either the number line or the formulas.

x = price of car B

x-130745 = difference in price from car A to car B

If x is the larger price, then x-130745 will be positive. If x is the smaller price, then x-130745 is negative.

In short,

x-130745 > 0 when x > 130745

x-130745 < 0 when x < 130745

Using absolute value will give us

|x-130745| = positive difference in price

The result of an absolute value is never negative

We write the |x-130745| > 10000 to indicate that the difference in price is more than 10000 dollar

 | x-130645 | > 10000

Part b.

We'll use the idea that if |x| > k, then x < -k or x > k

to get the following

|x-130745| > 10000

x-130745 < -10000 or x-130745 > 10000

x < -10000+130745  or  x > 10000+130745

x < 120745  or  x > 140745

Car B has a price less than $120,745

OR

Car B has a price greater than $140,745

So basically anything that is not between 120745 and 140745. The price has to be positive of course.

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1) Two points are the minimum number of points that need to be plotted to have instances of all four groups of numbers.

2) The sets that positive integers belong to among the available are;

possibilities

Choices A, B, C, and D

1) There are two basic categories into which numbers are often divided:

- Rational numbers

- Irrational numbers

The four examples above are all different categories of rational numbers.

Positive integers are now by definition also known as whole numbers and natural numbers. Whole numbers and natural numbers can therefore be displayed in one graphic.

Since integers may be both positive and negative, as well as include fractions, another plot will be needed to display them.

In order to plot the fewest number of points necessary to provide examples for each of the four sets of numbers

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If j(x) = 4^(x - 2), the solving the given expression [j(x + h) - j(x)]/h gives;

[j(x + h) - j(x)]/h = (4^(x - 2))(4^(h) - 1)]/h

We are given the function as;

j(x) = 4^(x - 2)

Now, we want to solve the expression;

[j(x + h) - j(x)]/h

This gives us;

j(x + h) = 4^(x - 2 + h)

Thus, our expression is now;

[j(x + h) - j(x)]/h = [4^(x - 2 + h) - 4^(x - 2)]/h

Now, according to laws of exponents, we know that;

y³ × y² = y³ ⁺ ²

Thus;

4^(x - 2 + h) = 4^(x - 2) × 4^h

Therefore;

[4^(x - 2 + h) - 4^(x - 2)]/h = (4^(x - 2))(4^(h) - 1)]/h

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This will be his initial investment. The amount for 8% will be 84000, and the amount for 12% will be 204000.

A mathematical statement known as an equation is made up of two expressions joined together by the equal sign. A formula would be 3x - 5 = 16, for instance.

When this equation is solved, we discover that the

value of the variable x is 7.

let x = the money invested at 8%

y = the money invested at 12%

an actor invests some money at 8% and 36,000 more than four times the amount at 12%

x = 36000 + 2y

total annual interest earned from the investment is 26400

0.08*x + 0.12*y = 26400

by solving the system of equations

x = 36000 + 2y

0.08*x + 0.12*y = 26400

solving the equations,

0.08(36000+2y)+0.12y=26400

2880+0.16y+0.12y=26400

y=84000

x=204000

The amount for 8% will be 84000, and the amount for 12% will be 204000.

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The correct answer is Tim

She drives at a variable speed for 2minutes

Answer:

1

Step-by-step explanation:

when there is no number, they are always 1.

1 multiplied by itself is always 1, so 1/1 is 1.

Hope this helps!

btw, brainliest if correct, ty!

Answer/Step-by-step explanation:

Simplify

 x⁻⁵

-------

 y³

Since the x on top has a negative exponent it must go down to the denominator.

So the answer would be:

 1

-------

x⁵y³

I hope this helps!

Answer:

See below

Step-by-step explanation:

48 + 3y = 90 degrees   so y = 14 degrees

3x + 2x + 12 = 90   so x = 78/5 = 15.6 degrees

P (B U C) is 0.1675 when B and C are independent and P (B U C) is 0 when B and C are mutually exclusive.

An Independent Event is defined as if the outcome of one event has no bearing on the outcome of the other, the two events are said to be independent events. Or, we may say that an event is considered independent if it does not affect the probability of another event. Probability-independent events mirror actual occurrences.

Let B and C be two events such that P(B) = 0.25 and P(C) = 0.67.

To determine P (B U C),

Given that B and C are independent.

Since B and C are independent events, we can just multiply the probabilities together, 0.25 × 0.67 = 0.1675

To determine P (B U C),

Given that B and C are mutually exclusive.

Since B and C cannot both occur at the same moment by definition because they are mutually exclusive, the answer is 0.

Therefore, P (B U C) is 0.1675 when B and C are independent and P (B U C) is 0 when B and C are mutually exclusive.

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To find h(-6), replace x = -6 into the function, as follows:

h(x) = -x - 3

h(-6) = -(-6) - 3

h(-6) = 6 - 3

h(-6) = 3

The expression used to depict area will be 9 / (3x - 1).

A rectangle may be defined as a closed figure with four sides and four interior angles. The interior angles are 90°.

The given expression for area = 27x - 9

Factorize 27x - 9

Taking 9 as greatest common factor outside, we get

27x - 9 = 9(3x - 1)

We know that the area of rectangle with dimensions length by breadth is given by:-

Area = Length x Breadth

Hence, the possible dimensions of the rectangle will be 9 / (3x - 1).

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Complete Question:

What are possible dimensions of the rectangular area at the right? if area is 27x-9.

Answer:

C

Step-by-step explanation:

- 2 = 5x + 3 ( subtract 3 from both sides )

- 5 = 5x ( divide both sides by 5 )

- 1 = x

First, simplify the expression:

Then:

To find the zero of the given expression, find the zero of -9x+30:

Therefore, the zero of the given expression is 10/3.

Answer:

use ASA

Step-by-step explanation:

since D=B, AB║CD

angle DEC=AEB (vertical angles)

AE=EC (given)

Jason, this is the solution:

Walter's daily wage = $ 50

Tips = 15% of the total cost of the dinner he serves

Tuesday earnings = $ 170

Therefore,

Tips = 170 - 50

Tips = 120

For finding the cost of the dinners, we use Direct Rule of Three, as follows:

Percentage Cost

15 120

100 x

_____________________

120 * 100 = 15 * x

12,000 = 15x

Dividing by 15 at both sides:

15x/15 = 12,000/15

x = 800

The total cost of the dinners Walter serverd on Tuesday was $ 800

The slope of the line that passes through the points (x1, y1) and (x2, y2) is computed as follows:

In this case, the line passes through the points (1,5) and (9,8)​, then its slope is:

According to the secant-tangent theorem, we have the following expression:

Now, we solve for x.

Then, we use the quadratic formula:

Where a = 1, b = 6, and c = -315.

Verify

REmember that the best deal is the deal with the less unit rate

so the order is

89 0z bottle is the best deal

64 oz cartoon

59 oz bottle

case of 24 10 oz bottles

10 oz bottle

therefore

Jason is not correct

Step-by-step explanation:

3x+4x-6=57

7x=63

x=9

AB=3x=3*9

AB=27

Hence, the coordinates of other point (x, y) are (0,6).

i.e.  (x, y) → (0,6)

Let AB be the segment where

The coordinate M(2, 9) and C(4, 12)

and we have to find the point E.

Let us assume the other point is (x, y)

As we know that

The midpoint is halfway between the two end points, meaning midpoint coordinates are basically termed as the average of the corresponding endpoint coordinates.

Mid - point formula:

m = [tex]\frac{x_{1}+x_{2} }{2}[/tex]

n = [tex]\frac{y_{1}+y_{2} }{2}[/tex]

So,

Substituting M(2, 9) into C(4, 12):

2 = [tex]\frac{4+x_{2} }{2}[/tex]

9 = [tex]\frac{12+y_{2} }{2}[/tex]

Solve the Equation:

[tex]x_{2} = 0\\y_{2} = 6[/tex]

Express solutions in ordered pairs:

(0,6)
Hence, the coordinates of other point (x, y) are (0,6).

i.e.  (x, y) → (0,6)

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The velocity of the body under simple harmonic motion is equal to - 5√3 / 2. (Correct choice: B)

Simple harmonic motion is a kind of self-sustained periodic motion that observed the following formula:

y = y' + Δy · cos ωt     (1)

Where:

The equation for the velocity of the body in simple harmonic motion is found differentiating (1):

v = - ω · Δy · sin ωt      (2)

If we know that ω = 1, t = 2π / 3 and Δt = 5, then the velocity of the body is:

v = - 1 · 5 · sin (2π / 3)

v = - 5 · sin (2π / 3)

v = - 5 · √3 / 2

v = - 5√3 / 2

The velocity is equal to - 5√3 / 2.

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Probability is expressed as

number of favorable outcomes/number of total outcomes

In a standard deck of cards, the total number of cards is 52.

There are 13 spades in a standard deck. Thus,

probability of selecting a spade = 13/52 = 1/4

There are 26 red cards in a standard deck of cards. Since the first card was replaced, the total number of cards remains 52.

probability of selecting a red card = 26/52 = 1/2

There are 4 queens in a standard deck of cards. Since the second card was also replaced, total number of cards is still 52. Thus,

Probability of selecting a queen = 4/52 = 1/13

Thus, the probability that the first card will be a spade, the second card will be a red card, and the third card will be a queen is

1/4 x 1/2 x 1/13

= 1/104

The number of integers from 31 to 40 is 10

Integers are the set of positive whole numbers and negative whole numbers including zero. Examples are 5, 81, -56, 9, -2, 0, 17 etc.

From the question, we are to determine the number of integers there are from 31 to 40.

First, we will list all the whole numbers from 31 to 40.

The whole numbers from 31 to 40 are

31, 32, 33, 34, 35, 36, 37, 38, 39, and 40.

All of these numbers are positive whole numbers. Thus, they are integers.

The number of integers listed above is 10.

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Answer:

Bds $ 1.98

Step-by-step explanation:

1386 bds / $ 700   *  $ 1 = 1.98 Bds

When a group of point is reflected across a line the distance of the points to the line must be equal, therefore the figure is inverted. With this in mind we can trace the intermediate step that is missing and finally draw the two lines.

Notice that the triangle get's inverted on each reflection around the lines.

The correct option regarding the minimum height reached by the toy is:

A height of -1.76 inches at 5.647 seconds.

The function for the height of the toy in the spring after x seconds is modeled as follows:

y = -cos(x) + 2cos(x)sin(x)

It is a trigonometric function, hence there is no rule to find the minimum value of the function as there is for a quadratic function, for example.

Since there is no rule, we have to sketch the graph of the function in the given domain of 0 < x < 6.

Using a graphing calculator, the graph of the function is given at the end of the answer, with minimum point at (5.647, -1.76), hence the correct option is:

A height of -1.76 inches at 5.647 seconds.

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The quadratic equation with roots -7, 3/4 in standard form is

4x² + 25x - 21 = 0.

A quadratic equation is an algebraic equation of degree two and has exactly two roots real or imaginary or complex.

We know the roots of a quadratic equation are also factors of a quadratic equation.

If x = a and x = b are two roots of a quadratic equation then x - a = 0 and

x - b = 0 are the factors of a quadratic equation that can be formed by multiplying the two factors (x - a)(x - b) = 0.

Given that -7 and 3/4 are the roots.

∴ { x - (-7)}{ x - 3/4) = 0.

(x + 7)(x - 3/4) = 0.

x² + 7x -(3/4)x - 21/4 = 0.

x² + (25/4)x - 21/4 = 0.

4x² + 25x - 21 = 0.

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mean = sum of the heights / number of grandchildren

The solution to the equation g(x) = 6x - 9 whenx = -8b is g(-8b) = -48b - 9

From the question, the equation of the function is given as

g(x) = 6x - 9

Also, we have the value of the variable to be

x = -8b

So, we substitute -8b for x in the equation of the function

g(x) = 6x - 9

The above equation becomes

g(-8b) = 6(-8b) - 9

Open the brackets in the above expression

g(-8b) = -48b - 9

The above equation cannot be firther simplified

Hence, the solution is g(-8b) = -48b - 9

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[tex]y=14x[/tex], where x is the number of gallons used and y is the distance driven in miles.