A box contains only green, red, blue and yellow counters. There is always at least one green counter amongst any 27 counters chosen from the box; always at least one red counter amongst any 25 counters chosen; always at least one blue amongst any 22 counters chosen and always at least one yellow amongst any 17 counters chosen. What is the largest number of counters that could be in the box?

(A) 27 (B) 29 (C) 51 (D) 87 (E) 91

Don't you dare say 91.

Answer: i think C sorry if i get it wrong :)

Step-by-step explanation:

Answer:

10 gallons of paint

Step-by-step explanation:

First, find the surface area of the monument.

From inspection, this is made up of 4 congruent rectangles and 4 congruent triangles.

Area of a rectangle = width x length

Therefore, area of one rectangle of the monument:

13 x 40 = 520 ft²

Area of triangle = 1/2 x base x height

Therefore, area of one triangle of the monument:

1/2 x 13 x 11 = 71.5 ft²

Therefore, total surface area of the monument

= 4 x SA of rectangle + 4 x SA of triangle

= 4 x 520 + 4 x 71.5

= 2080 + 286

= 2366 ft²

We are told that one gallon of paint can cover 239 ft², and that paint can only be bought by the gallon.

Divide the total surface area of the monument by the area one gallon of paint can cover to calculate how many cans of paint are needed.

2366 ÷ 239 = 9.89958159...

Therefore, 10 gallons of paint must be bought (since we need to round up as paint can only be bought by the gallon).

The correct answer is D. f(x) = 11x - 4 and g(x) = (x + 4)/11

To determine which pair of functions are inverses of each other, we need to check if the composition of the functions results in the identity function, which is f(g(x)) = x and g(f(x)) = x.

Let's test each option:

Option A:

f(x) = x/2 + 15

g(x) = 12x - 15

f(g(x)) = (12x - 15)/2 + 15 = 6x - 7.5 + 15 = 6x + 7.5 ≠ x

g(f(x)) = 12(x/2 + 15) - 15 = 6x + 180 - 15 = 6x + 165 ≠ x

Option B:

f(x) = ∛3x

g(x) = (x/3)^3 = x^3/27

f(g(x)) = ∛3(x^3/27) = ∛(x^3/9) = x/∛9 ≠ x

g(f(x)) = (∛3x/3)^3 = (x/3)^3 = x^3/27 = x/27 ≠ x

Option C:

f(x) = 3/x - 10

g(x) = (x + 10)/3

f(g(x)) = 3/((x + 10)/3) - 10 = 9/(x + 10) - 10 = 9/(x + 10) - 10(x + 10)/(x + 10) = (9 - 10(x + 10))/(x + 10) ≠ x

g(f(x)) = (3/x - 10 + 10)/3 = 3/x ≠ x

Option D:

f(x) = 11x - 4

g(x) = (x + 4)/11

f(g(x)) = 11((x + 4)/11) - 4 = x + 4 - 4 = x ≠ x

g(f(x)) = ((11x - 4) + 4)/11 = 11x/11 = x

Based on the calculations, only Option D, where f(x) = 11x - 4 and g(x) = (x + 4)/11, satisfies the condition for being inverses of each other. Therefore, the correct answer is:

D. f(x) = 11x - 4 and g(x) = (x + 4)/11

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By using the quadratic formula, the solution to this quadratic equation is equal to -0.5251 or -3.8081.

In Mathematics, a quadratic equation can be defined as a mathematical expression that can be used to define and represent the relationship that exists between two or more variable on a graph. In Mathematics, the standard form of a quadratic equation is given by;

ax² + bx + c = 0

Mathematically, the quadratic formula is modeled or represented by this mathematical expression:

\(x = \frac{-b\; \pm \;\sqrt{b^2 - 4ac}}{2a}\)

From the information provided, we have the following values;

3x² + 13x + 4 = 0

Where:

a = 3

b = 13

c = 4

Substituting the values into the quadratic formula, we have the following;

\(x = \frac{-(13)\; \pm \;\sqrt{(13)^2 - 4(3)(13)}}{2(3)}\\\\x = \frac{-13\; \pm \;\sqrt{169 - 72}}{6}\)

x = (-13 + √97)/6

x = -0.5251 or -3.8081.

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Answer:

get photomath

Step-by-step explanation:

Answer:

36 times

Step-by-step explanation:

Given

\(Red = 4\)

\(Total = 7\)

\(n = 63\)

See attachment

Required

Predicted number of times to land on red

First, we calculate the probability of landing on red

\(Pr = \frac{Red}{Total}\)

\(Pr = \frac{4}{7}\)

The predicted number of red is the =n calculated as:

\(Red = Pr * n\)

\(Red = \frac{4}{7}*63\)

\(Red = 4 * 9\)

\(Red = 36\)

Any alternative for the variable in a function that results in a zero answer is said to as the zero of a function.

The x-intercept(s) of the function's graph, or the real zero of a function, is where the function's graph hits the x-axis graphically.

The values of the variable in a function that allow the function to equal zero are termed the zeros of the function. The places on the x-axis where the graph crosses the x-axis are referred to as a function's zeros graphically. In other respects, we can say that the zeros of something like a function are the x-intercepts of the graph.

Finding the values of the variable that correspond to the function's zeros can be achieved by equating the function to 0. By calculating the polynomial and then equating it to 0, we can discover the zeros for polynomials.

Example:

Find the zeros of the function f(x) = ex - 1. Answer: Zero of function f(x) = ex - 1 is x = 0.

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Answer:

Step-by-step explanation:

1222235567899.99978..88694..6.4.4.6.4.4.5

the probability that at most 40 will get less than 40 seconds and at most 40 will get more than 40 seconds to solve the puzzle.

less than 40 seconds -  Event A

more than 40 sec  - A ' ( A bar / A compliment)

not

maximum number of people in Event A = 40

maximum number of people in A' = 40

total number of maximum people in A or A'  = 40 +40 = 80

but here there are 100 people > 80

hence

this is not possible

Required probability = 0

Probability is a branch of mathematics that quantifies the likelihood of an event occurring or the likelihood of a statement being true. The probability of an event is a number between 0 and 1, with approximately 0 indicating the improbability of the event and 1 indicating certainty.

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Answer:

5

Step-by-step explanation:

x/5=3/9

9x=45

x=45/9

x=5

Answer:

Cumulative Frequency:

The sum of all the frequencies for all classes is equal to the number of elements in the given data and that summation is termed as the cumulative frequency which defines the number of entries of that statistical data.

The sum of relative frequencies is also equal to one, since the sum of all fractional parts must equal the whole.

Step-by-step explanation:

Answer:

\(\frac{2}{7}\)

Step-by-step explanation:

Another name for 1 is \(\frac{7}{7}\)

\(\frac{7}{7}\) - \(\frac{5}{7}\) = \(\frac{2}{7}\)

The measures of the angles are ∠1 = 127°, ∠2 = 53°, ∠3 = 127°, ∠4 = 37°, ∠5 = 53°, ∠6 = 90°, ∠7 = 37°, ∠8 = 143°, ∠9 = 37° and ∠10 = 143°

From the question, we have the following parameters that can be used in our computation:

The transversal lines and the other lines

So, we have

∠1 = 180 - 53

Evaluate

∠1 = 127°

Also, we have

∠5 = 53°

By vertical angles, we have

∠2 = 53°

∠3 = 127°

Next, we have

∠4 = 127 - 90°

∠4 = 37°

Solving further, we have

∠6 = 90°

By corresponding angles, we have

∠7 = 37°

∠9 = 180 - 90 - 53°

∠9 = 37°

∠10 = 90 + 53°

∠10 = 143°

∠8 = 143°

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Answer:

28 i think

Step-by-step explanation:

51+47=98

98-12 the ones that flew away that takes it to 86

86/3 the 3 balloons buntch than is 28

p.s. i mght of got some equations wrong but this is what i got

Answer:

A

Step-by-step explanation:

Since we have y = 5, the only y value on the question that equals 5 is A.

There is a 42.3% chance that the Rangers will win a majority of their seven games against the Islanders, assuming their win percentage stays the same.

We can use the binomial distribution to calculate the probability of the Rangers winning a majority of their games against the Islanders, given their win percentage of 55.1%. Let's denote the probability of the Rangers winning a single game against the Islanders as p.

Since the Rangers and Islanders play seven games against each other, the number of games the Rangers win against the Islanders follows a binomial distribution with parameters n = 7 and p = 0.551.

To find the probability that the Rangers win a majority of these seven games, we need to sum the probabilities of all possible outcomes where they win four or more games. We can use the binomial probability formula to calculate each of these individual probabilities and then sum them up:

P(Rangers win 4 or more games) = P(Rangers win 4 games) + P(Rangers win 5 games) + P(Rangers win 6 games) + P(Rangers win 7 games)

\(= (7 choose 4) * 0.551^4 * (1 - 0.551)^3 + (7 choose 5) * 0.551 ^ 5 * (1 - 0.551)^2 + (7 choose 6) * 0.551^6 * (1 - 0.551) + (7 choose 7) * 0.551^7\)

Using a binomial calculator or a spreadsheet, we can evaluate this expression and find that:

P(Rangers win a majority of their games against the Islanders) = 0.423

Therefore, there is a 42.3% chance that the Rangers will win a majority of their seven games against the Islanders, assuming their win percentage stays the same.

The Binomial distribution is a discrete probability distribution that describes the probability of obtaining a certain number of successes in a fixed number of independent trials, where each trial can have only two outcomes (e.g., success or failure).

The distribution is defined by two parameters: the number of trials n and the probability of success in each trial p. The distribution gives the probability of obtaining k successes in n trials, where k can range from 0 to n.

The formula for the probability mass function of the Binomial distribution is:

\(P(k) = (n choose k) * p^k * (1 - p)^n-k\)

where (n choose k) is the binomial coefficient, which gives the number of ways to choose k items from a set of n items. The formula can be used to calculate the probability of obtaining k successes in n trials, given a fixed probability of success p.

The Binomial distribution is used in many areas of statistics, including quality control, epidemiology, and finance, among others. It is also a fundamental building block for more complex statistical models, such as the Poisson distribution and the normal distribution.

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Therefore, The value of E°cell for the reaction that occurs when current is drawn from this cell at standard conditions is 1.20 V.

Explanation: The given cell is a galvanic cell. The standard cell potential for this cell can be calculated using the Nernst equation.
Ecell = E°cell - (0.0592/n) log Q
Here, n = number of electrons transferred = 2
At standard conditions, Q = 1, as all species are at their standard states.
Thus,
Ecell = E°cell - (0.0592/2) log 1
Ecell = E°cell
The standard cell potential can be calculated using standard reduction potentials for the given half-reactions.
Zn2+(aq) + 2e- → Zn(s)   E° = -0.76 V
Fe2+(aq) + 2e- → Fe(s)    E° = -0.44 V
E°cell = E°reduction (cathode) - E°reduction (anode)
E°cell = 0.44 - (-0.76) = 1.20 V

Therefore, The value of E°cell for the reaction that occurs when current is drawn from this cell at standard conditions is 1.20 V.

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Answer: Each player will get 9 cards

Step-by-step explanation:

Given, there are 6 players and 58 cards.

i.e. Total players = 6 and total cards = 58

If each player is given the same number of cards, then by the division operation the number of cards each player will get = ( total cards) ÷ ( total players)

\(=58\div6\)    

\(=9\dfrac{2}{6}\)

Hence, each player will get 9 cards ( 2cards will be left).

The correct inequality representing the sentence is: 7.2 - n > 29.

A mathematical statement that claims two expressions are equal is known as an equation. Equations can be solved to get the value(s) of the variable(s) that make the equation true by using the equals symbol (=) to express equality. On the other hand, an inequality is a mathematical statement that says two expressions aren't always equal to one another but are instead greater or less than one another. Inequalities can be solved to determine the range of values of the variable that satisfy the given constraints. Inequalities employ symbols like, >,, and to express these relationships.

For the given statement the mathematical representation is given as: 7.2 - n > 29.

Hence, the correct inequality representing the sentence is: 7.2 - n > 29.

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The value of x is 30 degrees.

A right-angled triangle is a type of triangle that has one angle that measures exactly 90 degrees (a right angle). This angle is formed by the intersection of the two sides of the triangle that are perpendicular to each other, which are called the legs or the adjacent and opposite sides. The side opposite the right angle is called the hypotenuse, and it is always the longest side in the triangle. The other two sides are usually labeled as a and b, and are called the legs or the adjacent and opposite sides depending on which angle is being considered. The Pythagorean theorem, which states that the sum of the squares of the two legs of a right triangle is equal to the square of the hypotenuse, is one of the fundamental properties of right-angled triangles. Right-angled triangles have numerous practical applications in geometry, trigonometry, physics, and engineering.

We can use the trigonometric ratio of sine to find the angle x.

sin(x) = opposite/hypotenuse = PQ/PR = 48/96 = 1/2

Taking the inverse sine of both sides, we get:

x = sin^(-1)(1/2)

Using a calculator, we get:

x ≈ 30 degrees

Therefore, the value of x is 30 degrees.

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To find the angle that maximizes the area of an isosceles triangle with legs of length 1, we can use basic trigonometry.

Let's denote the angle between the base and one of the congruent legs as θ. Since the triangle is isosceles, the other congruent angle will also be θ.

The area of a triangle can be calculated using the formula: Area = (1/2) * base * height.

In this case, the base of the triangle is 1, and the height can be determined using trigonometry. The height is the side opposite the angle θ, and we can find it by using the sine function:

sin(θ) = opposite/hypotenuse

The hypotenuse of the triangle is also 1. Therefore, the height is sin(θ).

Now we can calculate the area in terms of θ:

Area = (1/2) * 1 * sin(θ)

To maximize the area, we can differentiate the area formula with respect to θ and find the critical points. However, we can simplify the problem by noting that the sine function is maximized when θ is π/2 (90 degrees) or 3π/2 (270 degrees).

So, the angle that maximizes the area of an isosceles triangle with legs of length 1 is θ = π/2 or 3π/2.

Converting to radians, the angle that maximizes the area is θ = π/2 radians.

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Answer:

46?

Step-by-step explanation:

Answer:

Step-by-step explanation:

9.48 as a mixed number in simplest form:

948/100

948/100= 948 ÷ 4/100 ÷ 4

948/100= 948 ÷ 4/100 ÷ 4= 237/25

948/100= 948 ÷ 4/100 ÷ 4= 237/25= 9 12/25

9 12/25 is the mixed number.

Answer:

9 beads

Step-by-step explanation:

for every 5 blue beads, she uses 1 orange bead.

if she uses 45 blue beads, divide by 5 to get the number of orange beads

1/5 = x/45

x = 9

hope this helps <3

Answer:

AB = 25 units

Step-by-step explanation:

In right triangle ACB, \( CD\perp AB\)

Therefore, by geometric mean property:

\(CD^{2} ={AD\times DB} \\ \\ {10}^{2} = AD\times 5 \\ \\ 100 = 5AD \\ \\ AD = \frac{100}{5} \\ \\ AD = 20\)

AB = AD + DB

AB = 20 + 5

AB = 25 units

The solution of the given system of linear equations is

x₁ = 3/2, x₂ = –2, x₃ = –1/2.

Given system of linear equations are 2x1-2x2+6x3 = 10x1+2x2-3x3 = 8-2x₁ x3 = -11

To solve the given system of equations, we have to compute A¹ and then use it to find x.To compute A¹, we have to follow these steps:

Step 1: Find the determinant of A:

Now we have matrix A:2 -2 6 1 2 -3 -2 0 1

So, we can find the determinant of A using the formula det(A) = (2×2) [(2×1)×(–3×1) + (6×2)×(1×–2) + (–2×2)×(2×–3)]  

= 4(–8 + (–24) + 24) = 4(–8) = –32

So, det(A) = –32

Step 2: Find the inverse of A:

We can find the inverse of matrix A using the formula A⁻¹ = adj(A) / det(A)

Here adj(A) is the adjoint matrix of A.

Now, we have to find the adjoint matrix of A.

Adjoint of A is given as:adj(A) = (cof(A))T

where cof(A) is the matrix of cofactors of the matrix A and (cof(A))T is the transpose of cof(A).

Now we can find cof(A) as:

cof(A) =   [[(-6) (-12) (-2)] [(6) (2) (2)] [(4) (8) (2)]]

Then transpose of cof(A), cof(A)T, is  

[[(-6) (6) (4)] [(-12) (2) (8)] [(-2) (2) (2)]]

So, adj(A) = cof(A)T

=  [[(-6) (6) (4)] [(-12) (2) (8)] [(-2) (2) (2)]

Now we can find A⁻¹ as:

A⁻¹ = adj(A) / det(A)

A⁻¹ = [[(-6) (6) (4)] [(-12) (2) (8)] [(-2) (2) (2)]] / (-32)

A⁻¹ =   [[(3/16) (-3/8) (-1/16)] [(3/4) (-1/4) (-1/4)] [(1/16) (-1/8) (1/16)]]

So, A¹ = A⁻¹ = [[(3/16) (-3/8) (-1/16)] [(3/4) (-1/4) (-1/4)] [(1/16) (-1/8) (1/16)]]

Then the given system of linear equations can be written as AX = B, where

X = [x₁ x₂ x₃]T and B = [10 8 –11]TAX = B  

⟹   X = A-¹B

Substituting the value of A-¹, we get X as   [[(3/16) (-3/8) (-1/16)] [(3/4) (-1/4) (-1/4)] [(1/16) (-1/8) (1/16)]] .

[10 8 -11]T= [3/2 -2 -1/2]T

So, the solution of the system is:

x₁ = 3/2x₂ = –2x₃ = –1/2

Therefore, the solution of the given system of linear equations is

x₁ = 3/2, x₂ = –2, x₃ = –1/2.

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Answer:

(11, 7) with an area of 128 in2.

Step-by-step explanation: