What value of x is in the solution set of the inequality –2(3x 2) > –8x 6? –6 –5 5 6

The number of marbles Ann had at the end is 54.

The percentage is calculated by dividing the required value by the total value and multiplying by 100.

Example:

Required percentage value = a

total value = b

Percentage = a/b x 100

Example:

50% = 50/100 = 1/2

25% = 25/100 = 1/4

20% = 20/100 = 1/5

10% = 10/100 = 1/10

We have,

Total marbles = 100

The number of marbles:

Marcy:

= 25% of 100

= 1/4 x 100

= 25

Roger:

= 21

Now,

The number of marbles:

Ann = 100 - (25 + 21) = 100 - 46 = 54

Thus,

Ann has 54 marbles at the end.

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Answer:

1/10

Step-by-step explanation:

There are 3 reds and 2 blues. He picks one and then another with no replacement. ? of getting 2 blues.

There are five marbles altogether.

First is 2/5

The second blue is 1/4

The chance of them both being blue is 2/5 * 1/4 = 2/20 = 1/10

Answer:

the answer is 3 option hope that it helps

Functions can be represented with equations, graphs and tables

The value of g(3) is 9

For x = 3, the equation of the function is:

g(x) = 2x + 3

So, we have:

g(3) = 2 * 3 + 3

Evaluate the product

g(3) = 6 + 3

Evaluate the sum

g(3) = 9

Hence, the value of g(3) is 9

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To prove that v = 0, we can use the properties of an inner product and the fact that {v₁, v₂, ..., vₙ} is an orthogonal basis of V.

Since {v₁, v₂, ..., vₙ} is an orthogonal basis, it means that for any i and j where i ≠ j, the inner product of vᵢ and vⱼ is zero. In other words, vᵢ⋅vⱼ = 0 for all i ≠ j.

Now, let's consider the inner product of v with itself: v⋅v.

Using the orthogonal property, we can expand v as a linear combination of the basis vectors: v = c₁v₁ + c₂v₂ + ... + cₙvₙ, where c₁, c₂, ..., cₙ are scalars.

Substituting this into the inner product, we have:

v⋅v = (c₁v₁ + c₂v₂ + ... + cₙvₙ)⋅(c₁v₁ + c₂v₂ + ... + cₙvₙ)

Expanding the inner product, we get:

v⋅v = (c₁v₁⋅v₁ + c₂v₂⋅v₂ + ... + cₙvₙ⋅vₙ) + (c₁v₁⋅v₂ + c₂v₂⋅v₃ + ... + cₙ₋₁vₙ₋₁⋅vₙ) + ...

However, since v is orthogonal to each vᵢ, except v itself, we have vᵢ⋅vⱼ = 0 for all i ≠ j. This means that all cross terms in the expansion will be zero.

Thus, we are left with:

v⋅v = c₁v₁⋅v₁ + c₂v₂⋅v₂ + ... + cₙvₙ⋅vₙ

Since v₁, v₂, ..., vₙ are orthogonal basis vectors, their inner products with themselves are nonzero. Therefore, v₁⋅v₁ ≠ 0, v₂⋅v₂ ≠ 0, ..., vₙ⋅vₙ ≠ 0.

For the inner product of v⋅v to be zero, it means that all the coefficients c₁, c₂, ..., cₙ must be zero. In other words, v = 0.

Hence, we have proven that if v is orthogonal to v₁, v₂, ..., vₙ, then v must be the zero vector.

The complete question is:

Let V be an inner product space, and let {v₁, v₂, ... vₙ} be an orthogonal basis of V. Let v ∈ V, and suppose that v is orthogonal to v₁, to v₂, ..., and to vₙ. Prove that v = 0

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The area of the farm that is too rough to use is 157.86

An object's area is how much space it takes up in two dimensions. In other terms, it's the measurement of the number of unit squares that are completely around the surface of a closed shape.

Let the total area of the farm be x.

Area of the farm, too rough to use=x/4

Area of farm kept for poultry farms=2x/5

Remaining Area=221

Thus,

\(x-(\frac{x}{4}+\frac{2}{5}x)=221\)

\(\\ x-\frac{13}{20}x=221\\\)

\(\frac{7}{20}x=221\\\)

x=631.43

Area of the farm too rough to use= 631.43/4

                                                        =157.86

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Answer:

B

Step-by-step explanation:

m<1 = 47

m<2= 34

Answer:

B

Step-by-step explanation:

The exterior angle of a triangle is equal to the sum of the 2 opposite interior angles.

122° is an exterior angle to both triangles , then

∠ 1 + 75° = 122° ( subtract 75° from both sides )

∠ 1 = 47°

and

∠ 2 + 88° = 122° ( subtract 88° from both sides )

∠ 2 = 34°

Answer:

The probability is 0.933

Step-by-step explanation:

We start by calculating the z-score

Mathematically;

z-score = (x-mean)/SD

x = 4

mean = 5.5

SD = 1

z-score = (4-5.5)/1 = -1.5

So we proceed to get the probability

This is;

P( z > -1.5)

we can get this from the standard normal distribution table

That will be

P(z > -1.5) = 0.93319

To the nearest thousandth, this is 0.933

18 responses would the company get over the course of the first 8 days after the magazine was published.

What is a geometric sequence?

A geometric progression, often referred to as a geometric sequence, is a series of non-zero values where each term following the first is obtained by multiplying the preceding value by a constant, non-zero number known as the common ratio.

Here, we have

Given: A large company put out an advertisement in a magazine for a job opening. On the first day, the magazine was published the company got 125 responses, but the responses were declining by 24% each day.

We apply here geometric sequence.

aₙ = arⁿ⁻¹

where

aₙ = n^{th} term of the sequence

r = is the common ratio

a = the first term of the sequence

a = 125

r = 100% - 24% = 76% = 76/100 = 0.76

aₙ = (125)(0.76)⁸⁻¹

aₙ = 125(0.76)⁷

aₙ = 18

Hence, 18 responses would the company get over the course of the first 8 days after the magazine was published.

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Answer:

463 (to the nearest whole number)

Step-by-step explanation:

We can model the given scenario as a geometric sequence.

The first term, a, is the number of responses the company got on the first day:

The common ratio is the number you multiply by at each stage of the sequence. As the responses are declining by 24% each day, then each day the responses are 76% of the previous day's responses, since 100% - 24% = 76%. Therefore, the common ratio, r, is:

To calculate the total responses the company would get over the course of the first 8 days after the magazine was published, use the Geometric Series formula.

\(\boxed{\begin{minipage}{7 cm}\underline{Sum of the first $n$ terms of a geometric series}\\\\$S_n=\dfrac{a(1-r^n)}{1-r}$\\\\where:\\\phantom{ww}$\bullet$ $a$ is the first term. \\ \phantom{ww}$\bullet$ $r$ is the common ratio.\\\end{minipage}}\)

Substitute a = 125, r = 0.76 and n = 8 into the formula and solve for S:

\(\implies S_8=\dfrac{125(1-0.76^8)}{1-0.76}\)

\(\implies S_8=\dfrac{125(1-0.111303478...)}{0.24}\)

\(\implies S_8=\dfrac{125(0.888696521...)}{0.24}\)

\(\implies S_8=\dfrac{111.087065...}{0.24}\)

\(\implies S_8=462.862771...\)

\(\implies S_8=463\)

Therefore, the total number of responses the company would get over the course of the first 8 days after the magazine was published is 463 to the nearest whole number.

The function f(x) = 150,000(0.85)^x can be used to determine the number of tickets the Houston Ballet Company will sell over time. In this function, the 150,000 represents the initial number of tickets sold before any time has passed (when x = 0).

It serves as the starting point or baseline for the exponential decay of ticket sales over time. As x increases, the function evaluates the number of tickets sold at a particular time, where each subsequent value of x represents a subsequent unit of time (such as days, weeks, months, etc.). The term (0.85)^x represents the decay factor, as it is less than 1 (0.85). Thus, the function models a situation where ticket sales decrease exponentially over time from the initial value of 150,000.

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Answer:

x = (9 ±√201) ÷ 12

Step-by-step explanation:

6x² -5x -9 = 0 ( rearranged)

a = 6  b = -5  c = -9

- - 9 = 9

-9² = 81 (the 81 must be positive, this is one error)

-4 x 6 x -5 = 120 ( the 5 must be a minus number, this is one error)

120 + 81 = 201

x = (9 ±√201) ÷ 12

Answer:

hexagonal based pyramid

E

7 faces

12 edges

7 vertex

13

15

Hope it helps :)

Answer:

Step-by-step explanation:

4 x 3 + 3 x 5 - 13: 7

12+15-62748517

=-62748490

Answer:

I think it is 5m + 4....

Step-by-step explanation:

Still confusing... i-ready as always...

Answer:

5m + 4

Step-by-step explanation:

First distribute, so 5(m + 1) is 5m + 5 (5 times m a plus 5 times 1)

Then you are left with 5m + 5 - 1

You do 5 - 1 which is equal to 4

The final answer is 5m + 4

50.

Rounding 50 to the nearest 10 is like doing nothing. 50 is already in the spot.

Hope this helps :)

Answer:

10

Step-by-step explanation:

i think so it may helps you

Answer:

Step-by-step explanation:

Use Pythagorean:

The surface area that can be painted with one complete rotation of the roller is 1508 inches².

Surface area is defined as the total amount of area that covers the surface or outside of a three-dimensional figure.

A paint roller is in the shape of a cylinder. To determine the surface area that can be painted with one complete rotation of the roller, solve for the surface area of a cylinder without the circular bases.

SA = 2πrh

where SA = surface area

r = radius of the base = 8 inches

h = height of the cylinder = width = 30 inches

Plug in the values and solve for the surface area.

SA = 2πrh

SA = 2π(8*30)

SA = 150.7.966 = 1508 inches²

Hence, the surface area that can be painted with one complete rotation of the roller is 1508inches².

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Answer: First secutitys at my school dont even have nothing but a walkie talkies in there hands but I will say this we have cops walking around inside of our school and there all armed up because obvisouly their cops so i would think not security should not have a fire arm because what happens if a old lady a securrityguard she cant move fast so I think not they would have to deal it with by hand and there walkie talkies.

Step-by-step explanation:

Answer:no because they might be part of a crime and shoot up the school like boom bang bin bot pow and 500 people drop dead like me in the bed room.

Step-by-step explanation:

Answer:

140in or 11.6 ft

Step-by-step explanation:

2 times 10 equals 20 so you would time 14 by ten to get the inches

The functions f(x) and g(x) are different functions

The function f(x) is a cubic function, while the function g(x) is a logarithmic function.

The common feature in both functions is their range

According to the statement

we have given that the some functions and we have to justify these functions.

The functions are given as:

f(x) = x³ + x² - 2x + 3 and g(x) = log(x) + 2

This means that the function f(x) is a cubic function, while the function g(x) is a logarithmic function.

The common key features of the functions

To do this, we plot the graphs of both functions

From the attached graph, we have the following features:

Function f(x)

Domain: -∞ < x < ∞

Range: -∞ < y < ∞

y - intercept = 3

x - intercepts = -2.37

Function g(x)

Domain: x > 0

Range: -∞ < y < ∞

y - intercept = None

x - intercepts = 0.01

By comparing the key features above, we can conclude that the common features in both functions is their range.

The functions f(x) and g(x) are different functions

The function f(x) is a cubic function, while the function g(x) is a logarithmic function.

The common feature in both functions is their range

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we can use the proportion: (Number of votes received by the candidate) / (Total number of votes) = 43% / 100%. the candidate received approximately 37.41 votes.

In the given local election, the candidate received 43% of the votes. To determine the number of votes they obtained, we need to use a proportion. A proportion is an equation that states that two ratios are equal.

Let's represent the number of votes received by the candidate as "x." The total number of votes cast in the election is stated as 87.

We can set up the proportion:

x / 87 = 43% / 100.

To solve for "x," we can cross-multiply:

100 * x = 43% × 87.

Simplifying further, we have:

x = (43/100) × 87.

By multiplying the fraction (43/100) by 87, we can determine the number of votes received by the candidate. Evaluating this expression, the candidate received approximately 37.41 votes.

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(a) The equilibrium point is approximately (26, 26) where quantity (x) and price (P) are both 26.

(b) Consumer surplus ≈ 434

(c) 434 dotars (d)  -1155 dotars.

To calculate the deadweight loss, we need to find the area between the supply and demand curves from the equilibrium quantity to the quantity \(x_C\).

To find the equilibrium point, we need to set the demand and supply functions equal to each other and solve for the quantity.

Demand function: D(x) = 61 - x
Supply function: S(x) = 22 + 0.5x

Setting D(x) equal to S(x):
61 - x = 22 + 0.5x

Simplifying the equation:
1.5x = 39
x = 39 / 1.5
x ≈ 26

(a) The equilibrium point is approximately (26, 26) where quantity (x) and price (P) are both 26.

To find the point (\(x_C\), \(P_C\)) where the price ceiling is enforced, we substitute the given price ceiling value into the demand function:

P_C = $30
D(\(x_C\)) = 61 - \(x_C\)

Setting D(\(x_C\)) equal to \(P_C\):
61 - \(x_C\) = 30

Solving for \(x_C\):
\(x_C\) = 61 - 30
\(x_C\) = 31

(b) The point (\(x_C\), \(P_C\)) is (31, $30).

To calculate the new consumer surplus, we need to integrate the area under the demand curve up to the quantity \(x_C\) and subtract the area of the triangle formed by the price ceiling.

Consumer surplus

\(=\int[0,x_C] D(x) dx - (P_C - D(x_C)) * x_C\\=\int [0,x_C] (61 - x) dx - (30 - (61 - x_C)) * x_C\\=\int [0,31] (61 - x) dx - (30 - 31) * 31[61x - (x^2/2)]\)
evaluated from

0 to 31 - 31[(61*31 - (31²/2)) - (61*0 - (0²/2))] - 31[1891 - (961/2)] - 311891 - 961/2 - 311891 - 961/2 - 62/2(1891 - 961 - 62) / 2868/2
Consumer surplus ≈ 434

(c) The new consumer surplus is approximately 434 dotars.

To calculate the new producer surplus, we need to integrate the area above the supply curve up to the quantity \(x_C\).

Producer surplus \(= (P_C - S(x_C)) * x_C - \int[0,x_C] S(x) dx(30 - (22 + 0.5x_C)) * x_C - \int[0,31] (22 + 0.5x) dx(30 - (22 + 0.5*31)) * 31 - [(22x + (0.5x^2/2))]\)
evaluated from 0 to 31(30 - 37.5) * 31 - [(22*31 + (0.5*31²/2)) - (22*0 + (0.5*0²/2))](-7.5) * 31 - [682 + 240.5 - 0](-232.5) - (682 + 240.5)(-232.5) - 922.5-1155
(d) The new producer surplus is -1155 dotars. (This implies a loss for producers due to the price ceiling.)

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Answer:

Step-by-step explanation:

Given:

Isolate the term of x from one side of the equation.

Use the distributive property.

DISTRIBUTIVE PROPERTY:

\(\Longrightarrow: \sf{A(B+C)=AB+AC}\)

Each term within the parentheses can be multiplied by a factor outside the parentheses.

3(x+1)

3*x=3x

3*1=3

Rewrite the expression down.

3x+3

3x+3+2(3x+4)

Multiply expand.

2(3x+4)

2*3x=6x

2*4=8

6x+8

3x+3+6x+8

Combine like terms.

3x+6x+3+8

Add the numbers from left to right.

3+8=11

3x+6x+11

Add.

Solutions:

3x+6x=9x

\(\Longrightarrow: \boxed{\sf{9x+11}}\)

I hope this helps. Let me know if you have any questions.

Answer:

its A i think\

Step-by-step explanation:

Answer:

around 17 mistakes

Step-by-step explanation:

We can write a ratio to solve

54 words             300 words

------------------ = -------------------

3 mistakes             x mistakes

Using cross products

54x = 3*300

54x = 900

Divide by 54

54x/54 = 900/54

x =50/3

x = 16.66666666(repeating)

around 17 mistakes

X = mistakes in 300 words

54/3 = 300/X

54X = 3 x 300

X = 900/ 54

X = about 17 words, since 16 and 2/3 rounded to the nearest tenth is 17

The right triangle is assumed to be inscribed in the rectangle, such that

hypotenuse is the diagonal of the rectangle.

Reasons:

Let x and y represent the length of the sides of the rectangle

Whereby the base and height of the right triangle are the same as the

length and width of the rectangle, we have;

Perimeter of the rectangle = 2·x + 2·y = 68

Therefore;

\(\displaystyle x + y = \frac{68}{2} = 34\)

x + y = 34

The base of the right triangle = x

The height of the right triangle = y

By Pythagoras's theorem, the length of the hypotenuse side = √(x² + y²)

Therefore; Perimeter of the right triangle = x + y + √(x² + y²) = 60

Which gives;

∴√(x² + y²) = 60 - (x + y) = 60 - 34 = 26

The length of the hypotenuse side, √(x² + y²) = 26 cm

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Answer:

a. 9.42 hours   b. $116.50

Step-by-step explanation:

The time in hours would be 9.42. Since it's 9 hours and 25 minutes, you find the answer by adding 9 + (25 min/60 min).

The gross pay would be ($11.50 * 8) + ($17.25 * 1.42). This is 92 + 24.495 = $116.50 total gross pay for Monday. The number 17.25 comes from the regular pay -- $11.50/h -- times 1.5 (since it's 1 1/2 the regular rate for over time), and the 1.42 comes from 9.42 h - 8 h, since the first 8 hours Lisa is paid the regular rate and any hours over that are the overtime rate.

a. The margin of error for the proportion of all adults who think things are going in the wrong direction for 90% confidence is 0.017.

b. The correct choice is: "We are 90% confident that the observed proportion of adults that responded 'wrong track' is within 0.017 of the population proportion."

a) To calculate the margin of error for a 90% confidence interval, we need to use the formula:

\(ME = z\sqrt{ (pq/n) }\)

where:

z = the z-score for a 90% confidence interval, which is 1.645

p = the proportion of adults who said things were going in the wrong direction, which is 0.44

q = the complement of p, which is 1 - 0.44 = 0.56

n = the sample size, which is 2306.

Plugging in these values, we get:

ME = 1.645sqrt(0.440.56/2306) = 0.017

Therefore, the margin of error for the proportion of all adults who think things are going in the wrong direction for 90% confidence is 0.017.

b) The correct choice is: "We are 90% confident that the observed proportion of adults that responded 'wrong track' is within 0.017 of the population proportion."

This means that if we were to conduct the same survey many times and calculate the confidence interval each time, we would expect 90% of those intervals to contain the true proportion of adults who think things are going in the wrong direction.

The margin of error of 0.017 indicates the maximum amount by which the sample proportion may differ from the true population proportion.

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All the points in both sets satisfy the constraints, the feasible solution is α = (1, 0, 0, 0) and β = 0. This plane separates the sets S1 and S2.

To formulate the problem as a linear optimization problem (LO), we can introduce slack variables to represent the signed distances of the points from the plane αTx = β. Let's denote the slack variables as y_i for points in S1 and z_i for points in S2.

1.1 Formulation:

The problem can be formulated as follows:

Minimize: 0 (since it is a feasibility problem)

Subject to:

α1x1 + α2x2 + α3x3 + α4x4 - β ≥ 1 for (x1, x2, x3, x4) in S1

α1x1 + α2x2 + α3x3 + α4x4 - β ≤ -1 for (x1, x2, x3, x4) in S2

α1, α2, α3, α4 are unrestricted

β is unrestricted

y_i ≥ 0 for all points in S1

z_i ≥ 0 for all points in S2

The objective function is set to 0 because we are only interested in finding a feasible solution, not optimizing any objective.

1.2 Finding a feasible solution:

To find a feasible solution for this linear optimization problem, we need to check if there exists a plane αTx = β that separates the given sets of points S1 and S2.

Let's set α = (1, 0, 0, 0) and β = 0. We choose α to have a non-zero value for the first component to satisfy α ≠ (0, 0, 0, 0) as required.

For S1:

(1, 2, 1, -1) - 0 = 3 ≥ 1, feasible

(3, 1, -3, 0) - 0 = 4 ≥ 1, feasible

(2, -1, -2, 1) - 0 = 0 ≥ 1, not feasible

(7, -2, -2, -2) - 0 = 3 ≥ 1, feasible

For S2:

(1, -2, 3, 2) - 0 = 4 ≥ 1, feasible

(-2, π, 2, 0) - 0 = -2 ≤ -1, feasible

(4, 1, 2, -π) - 0 = 5 ≥ 1, feasible

(1, 1, 1, 1) - 0 = 4 ≥ 1, feasible

Since all the points in both sets satisfy the constraints, the feasible solution is α = (1, 0, 0, 0) and β = 0. This plane separates the sets S1 and S2.

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