6. Four friends are going into business together and have agreed to evenly
split the rental cost of their new company's office space. Each friend
wants to pay no more than $80 per month for their share of the rental
cost. What inequality represents the situation, where x is the total cost of
renting the office space?

The recursive sequence that would produce the sequence 5, -17, 71, is by multiplying the previous term by -4 and adding 3.

A recursive sequence is a sequence where each term is defined as a function of the preceding term(s).

Given the sequence 5, -17, 71, ..., we can see that the next term in the sequence is obtained by multiplying the previous term by -4 and adding 3.

Therefore, the recursive sequence that produces this sequence is:

a_1 = 5

a_n = -4a_{n-1} + 3 where n > 1

This means that the first term of the sequence is 5, and each subsequent term is obtained by multiplying the previous term by -4 and then adding 3.

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The approximate range will be 56.25 gm. after the end of 3 years.

As per the question,

We have, the value of the weight of the bacteria = 450 gm

As the rate of bacteria is decreasing with rate of 1/2

So, after 1 year the number of bacteria will be half as it was at the start of the year.

So, the number of bacteria after 1 year will be = 450 *(1/2)=225

As the rate of bacteria is again decreasing with the rate of 1/2

So, after 2 years the number of bacteria will be half as it was at the start of the year.

So, the number of bacteria after 2 years will be = 225 *(1/2)=112.5

As the rate of bacteria is decreasing with the rate of 1/2

So, after 3 year the number of bacteria will be half as it was at the start of the year.

So, the number of bacteria after 3 years will be = 112.5*(1/2)=56.25

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Answer: 4.53

Step-by-step explanation:

10 times less than 45.3 means that you will be looking for an answer that is the solution to 45.3 / 10, which equals 4.53.

Answer:

A. 33 • 18

Step-by-step explanation:

Product means multiplication

There are different symbols that are used for denoting multiplication and the dot (•) symbol is one of them

So 33 • 18 is same as 33 x 18 which is the product of 33 and 18

The coordinates of upper R prime are  (-2, 4).

Now, According to the question:

Rotation describes the circular motion of an object around its center. There are different ways things can rotate. Rotation of the Earthre. A very familiar kind of rotation is when a spherical, three-dimensional object turns around an invisible line inside its center.

The sails center of rotation is the origin (0,0)

The top of one sails point R(2, -4).

A 180 degree rotation make you turn (x, y) into (-x, -y),

So, the point  turn (2,-4 ), into (-2, 4).

Therefore the coordinates of R are  (-2, 4).

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Answer:

112.8 hours / 12 days

112.8/12 = average of 9.4 hours per day

The percent of Hector's net pay that is automatically withdrawn for savings is  7. 95 %

To find the percentage of Hector's net pay that is being withdrawn for savings in an automatic manner, the formula is:

= Amount withdrawn for savings / Pay before amount is withdrawn x 100 %

Amount withdrawn for savings = $ 122

Pay before amount is withdrawn :
= 1, 413 + 122

= $ 1, 535

The percentage withdrawn is :

= 122 / 1, 535 x 100%

= 7. 95 %

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A linear equation representing the data in table is t(n) = 12x + 23.

The missing values in table should be completed as follows;

n            t(n)

4             71

5             83

Mathematically, the point-slope form of a straight line can be calculated by using this mathematical expression:

y - y₁ = m(x - x₁) or y - y₁ = (y₂ - y₁)/(x₂ - x₁)(x - x₁)

Where:

m represents the slope.

x and y are the data points.

Next, we would determine the linear equation representing the data in table which passes through the points (1, 24) and (2, 36) by using the point-slope form as follows:

y - y₁ = (y₂ - y₁)/(x₂ - x₁)(x - x₁)

y - 24 = (36 - 24)/(2 - 1)(x - 1)

y - 24 = 12(x - 1)

y = 12x - 1 + 24

y = t(n) = 12x + 23

When the value n = 4, the value of t(n) can be calculated as follows;

t(4) = 12(4) + 23

t(4) = 71.

When the value n = 5, the value of t(n) can be calculated as follows;

t(5) = 12(5) + 23

t(5) = 83.

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David's method to find the height of the tree is the use of the properties of similar triangles. The height of the tree is approximately 24 feet

According to the laws of reflection, we have;

Angle of incidence of the light from the top of the tree = Angle of the reflected light ray David sees.

The possible values in the question are;

Distance of the mirror from the tree = 37 feet

Distance from where David is standing to the mirror = 9.3 ft.

Height of his eyes above the ground = 6 ft.

Required: Height of Tree

Therefore;

The triangle formed by David's height, the reflected ray from the mirror and his distance from the mirror is similar to the right triangle formed by the tree, which by the relationship of similar triangles, gives;

[tex]\frac{9.3}{37}[/tex] = [tex]\frac{6}{Height of the Tree}[/tex]

Height of the tree × 9.3 = 6 × 37

Height of the tree = [tex]\frac{6 X 37}{9.3}[/tex] = 23.87 ≅ 24 feet

Therefore, the tree is approximately 24 feet tall

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This data's linear regression equation is y = mx + b, where y is the quantity of chicken feed, x is the number of months since March, m is the line's slope (or the rate at which y changes with respect to x), and b is the y-intercept (or the value of y at x = 0).

The pace at which the amount of chicken feed has been decreasing over time is seen by the slope of the line. The beginning quantity of chicken feed in the barn in March is represented by the y-intercept.

Based on the rate of reduction and beginning quantity for each month since March, the linear regression equation may be used to forecast the amount of chicken feed in the barn in the issue situation.

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Answer:

[tex]\sf x=11+11i\\x=11-11i[/tex]

Step-by-step explanation:

Given quadratic equation:

[tex]\sf -108=(x-11)^2+13[/tex]

Subtract 13 from both sides:

[tex]\implies \sf -108-13=(x-11)^2+13-13[/tex]

[tex]\implies \sf -121=(x-11)^2[/tex]

Switch sides:

[tex]\implies \sf (x-11)^2=-121[/tex]

[tex]\textsf{For $(g(x))^2=f(a)$ the solutions are $g(x)=\pm\sqrt{f(a)}$}[/tex]

[tex]\implies \sf x-11=\pm \sqrt{-121}[/tex]

Rewrite -121 as 11² · -1 :

[tex]\implies \sf x-11=\pm \sqrt{11^2 \cdot-1}[/tex]

[tex]\textsf{Apply radical rule} \quad \sqrt{ab}=\sqrt{a}\sqrt{b}:[/tex]

[tex]\implies \sf x-11=\pm\sqrt{11^2} \sqrt{-1}[/tex]

[tex]\implies \sf x-11=\pm11\sqrt{-1}[/tex]

[tex]\textsf{Apply\;imaginary\;number\;rule}:\quad \sqrt{-1}=i[/tex]

[tex]\implies \sf x-11=\pm11i[/tex]

Add 11 to both sides:

[tex]\implies \sf x=11\pm11i[/tex]

Therefore, the solutions are:

[tex]\implies \sf x=11+11i[/tex]

[tex]\implies \sf x=11-11i[/tex]

Answer:

The expression (quotient) which is modelled by the given diagram as in the task content is; (x²+x-2)/(x-1) = x +2.

Which expression and quotient is depicted by the diagram model as in the task content?

It follows from the task content that the diagram model in discuss by observation involves a quotient in which case, the division is; (x-1).

Additionally, the dividend in the quotient by observation is the sum of terms as follows;

x² + x +x -x -1 -1 = x²+x -2.

Ultimately, the result of the division according to the model is; (x +2).

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Step-by-step explanation:

So, there are 52 ways to draw two cards such that the first card is a spade and the second card is a queen.

In a standard 52-card deck, there are 13 cards of each suit: spades, hearts, diamonds, and clubs. Each suit has 4 face cards (Jack, Queen, King, and Ace) and 9 numbered cards (2 through 10).

To find the number of ways to draw two cards such that the first card is a spade and the second card is a queen, we first need to determine the number of spades in the deck, and then the number of queens.

There are 13 spades in a standard 52-card deck, so there are 13 ways to draw a spade as the first card.

There are 4 queens in a standard 52-card deck (one from each suit), so there are 4 ways to draw a queen as the second card.

To find the total number of ways to draw two cards such that the first card is a spade and the second card is a queen, we multiply the number of ways to draw each card: 13 * 4 = 52 ways.

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As an alternative, we could contend that the probability of the first coin coming up heads or tails is 1/2, the probability of the second coin coming up heads or tails is 1/2, and so on for the third and fourth coins.

This would reduce the probability of any given sequence of heads and tails to (1/2)x(1/2)x(1/2)x(1/2)=(1/16).

The curve achieves its greatest value for N=2 heads, which is the case where the outcome is most likely. This is exactly what you would anticipate: if each coin has an equal chance of landing heads or tails, then in four flips, half of the results should be heads, making N = 4x(1/2) = 2 the most likely result.

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Answer:

Answer is in attached photo.

Step-by-step explanation:

Solution is in attached photo, this question is testing on function substitution. (Substituting an input to get an output.)

Answer:

A.

Step-by-step explanation:

4x² is a perfect square because it is (2x)²

9 is a perfect square with a value of 3

so if we factor 4x² - 9 we can use the difference of two squares to get:

(2x+3)(2x-3)

Answer:

False

Step-by-step explanation:

Answer come only two

The number of occupied rooms is 140 rooms

Percentage can be defined as a ratio or number that is expressed as a fraction of the number, 100.

It is denoted the the percent sign, "%"

Percentage is known as a dimensionless number. This means that is it has no unit of measurement.

They can also be represented in fraction or decimal forms, like 0.3%, 0.5%, etc

From the information given, we have that;

The number of occupied rooms is;

= 16/100 × 875

Find the fraction

=0. 16 × 875

multiply the values

= 140 rooms

Hence, the value is 140 rooms

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Answer: No real "space" exists. There is plenty of air all around us

Step-by-step explanation: I'm sorry If I am wrong tysm

-☈⊙⌘☿

Answer:

cosmic microwave background radiation

Step-by-step explanation:

The train travels an average 12 miles/hr

We always need to be working in the same units, so lets convert the trains speed to minutes since the time traveled is in minutes.

12 miles / 60 min = 0.2 miles/min

The part containing the sum of two terms in the given expression can be found to be as (3 + 4) and (6 + 8) respectively.

An algebraic expression can be obtained by doing mathematical operations on the variable and constant terms.

The variable part of an algebraic expression can never be added or subtracted from the constant part.

here, we have,

The given expression is 2(3 + 4).

It can be rewritten as follows,

2(3 + 4)

=2 × 3 + 2 × 4

=6 + 8

or, 2 × 7

Thus, in order to find the expression for sum of two terms in the given expression, there can be two possible ways, the first is (3 + 4) and the other is (6 + 8).

Hence, the sum of two terms in the given expression is found to be as (3 + 4) and (6 + 8) respectively.

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The probability of landing on purple is equal to the probability of landing on yellow. Therefore, option D is the correct answer.

Probability can be defined as the ratio of the number of favourable outcomes to the total number of outcomes of an event.

We know that, probability of an event = Number of favourable outcomes/Total number of outcomes

Given that, a spinner divided into eight equal colored sections, with one orange, two purple, two yellow, and three blue.

Here,

Probability of landing on orange is 1/8

Probability of landing on purple is 2/8 =1/4

Probability of landing on yellow is 2/8 =1/4

Probability of landing on blue is 3/8

Therefore, option D is the correct answer.

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You need to drive 122.86 km/ h to driving from Vegas to los Angeles in 3.5 hours

It is a physical quantity that indicates the displacement of a mobile per unit of time, it is expressed in units of distance per time, for example (miles/h, km/h).

The formula and procedure we will use to solve this exercise is:

v = x /t

Where:

Information about the problem:

Applying the velocity formula, we get:

v = x /t

v = 430 km / 3.5 h

v = 122.86 km/ h

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The probability that the result was a 6 is P(A)=1/3 the die is tossed and we are told that a result is a number greater than 4.

A standard 6-sided die numbered 1 to 6 has 2 sides that meet the criterion of greater than 4, which are 5 and 6. So out of 6, there are 2 ways.

A die has 6 faces with the numbers 1,2,3,4,5 and 6 on each of the six faces. Now consider an unbiased die and the probability of any of the faces appearing in a single roll is 1/6.

So,

P(1)=P(2)=P(3)=P(4)=P(5)=P(6)=1/6

The numbers that are greater than 4 are 5 and 6

So it can be P(5) or P(6)=

P(5)+P(6)=2/6=1/3.

If you had stated at least a 4, then there are three chances which are to be 4,5,6 that meet the criterion, and the chance would be 3/6=1/2.

Hence, by the classical definition of probability, the probability of getting a number more than 4 in a single throw of a die is 1/3.

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7/6 = 28/x

To solve for x, you can cross-multiply:

7 * x = 6 * 28

Simplifying:

x = 6*28/7

x = 24

So, you would need 24 cups of milk.

Answer:

28 cups of sugar / 7 parts of sugar = 4 cups

If 4 cups is 1 part, 6 parts of milk would be 4 x 6

4 x 6

= 24

You would need 24 cups of milk.

Based on the given percentages, the number of adult American men who think the federal government should fund stem cell research is 67,860,000.

The percentage is the ratio of a value in relation to another.

The percentage is determined as the quotient of the numerator divided by the denominator, multiplied by 100.

The percentage of men who approve of stem cell research = 58%

The percentage of men who do not approve of the research = 39%

The percentage of men who have no opinion on the research = 3%

The estimated number of adult American men = 117,000,000

Thus, based on the percentage of men who approve of stem cell research, the number is 67,860,000. (117,000,000 x 58%).

Federal Government Funding of Stem Cell Research

                          Total      Men     Women

Should fund       55%       58%        52%

Should not fund 41%       39%         44%

No opinion          4%          3%           4%

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The total price he has to pay for the clothes is 27.83

What is Percentage ?

Percentage can be defined as the product ratio of given value, total value and hundred.

Clothing price (100 percent) is 26 dollars and 50 cents, Added tax is 5 percent, and total cost is blank.

Darrien purchases some clothes for a total of $26.50, before tax. Sales tax in his state is 5 percent.

If Darrien spends 26.50, multiply that by 0.05 (26.50×0.05)

which is 1.325 which rounds to 1.33. $1.33 is the amount of tax he has to add. For the full price you would do 26.50+1.33 to get 27.83.

Therefore, The total price he has to pay for the clothes is 27.83

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Answer: 40°

Step-by-step explanation:

x^-4/x^3 times x^-7 in equivalent expression is x⁻¹⁴

The index form of a number can be defined as the number that is written as an exponential expression.

It is also seen as the single number that is raised to another number.

The rules of index forms are;

From the information given, we have that;

x⁻⁴/x³ × x⁷

Since the denominators are of the same base, add the powers

x⁻⁴/x³⁺⁷

Add the values

x⁻⁴/x¹⁰

Now, subtract the powers

x⁻¹⁴

Hence, the value is x⁻¹⁴

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