mateo is playing a word game where he's trying to make 444-letter words by rearranging the letters in the word iron. how many unique ways are there to arrange the letters in the word iron?

Answer:

13 × 10 = 130 ( it's a rectangle)

5² π /2 ≈ 12.5 × 3.14 = 39.25 ( semicircle)

130 + 39.25 = 169.25 ≈ 170

The explicit formula of the sequence is (b) a(n) = 8 - 2(n - 1)

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

a₁ = 8,

aₙ = aₙ₋₁ - 2

In the above sequence, we can see that the 2 is subtracted from the previous term to get the current term

This means that

first term, a = 8

common difference, d = -2

The nth term is then represented as

a(n) = a + (n - 1)d

Substitute the known values in the above equation, so, we have the following representation

a(n) = 8 + (n - 1) * -2

Evaluate

a(n) = 8 - 2(n - 1)

Hence, the explicit is (b) a(n) = 8 - 2(n - 1)

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The system of linear equations, y = -x + 1 ; 2y = -2x + 2 has infinite many solutions so it is dependent Consistent .

A system of linear equations consists a pair of equations with same variable. An ordered pair that satisfies all equations of the system is the solution of the system. A linear system of equations is consistently dependent if there are infinitely many solutions. In this case, the system line graph is the same. That is, the equations for the system represent the same line. We have System of equations ,

y = -x + 1 => x + y -1 = 0--(1)

2y = -2x + 2 => 2x + 2y -2 = 0 --(2)

Comparing the equation (1) with standard equation a₁x + b₁y + c₁z = 0 and equation (2) with

a₂x + b₂y + c₂z = 0 , we get

a₁ = 1 , b₁ = 1 , c₁ = -1 , a₂ = 2 , b₂ = 2 , c₂= -2

Now, we check the ratio of coefficients

a₁/a₂ = 1/2 , b₁/b₂= 1/2 , c₁/c₂= -1/-2 = 1/2

=> a₁/a₂ = b₁/b₂= c₁ /c₂

Thus, the lines are coincide with each other then there exist infinite number of solutions since, a line has infinite points. In such a case, the pair of lines is said to be dependent and consistent. Therefore, system of equations is dependent and consistent.

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Answer:

Step-by-step explanation:

Let x be the number that went in,

[x(1+50%)]x(1-5%)=57
x(1+50%)=60

x=40

The solution is, the number went in is 40.

A percentage is a number or ratio that can be expressed as a fraction of 100. A percentage is a number or ratio expressed as a fraction of 100. It is often denoted using the percent sign, "%", although the abbreviations "pct.", "pct" and sometimes "pc" are also used. A percentage is a dimensionless number; it has no unit of measurement.

here, we have,

given that,

when a number Increase by 50% & Decrease by 5%,

then, A number went into this machine and 57 came out.

Let x be the number that went in,

so, using the given condition, we get,

[x(1+50%)]x(1-5%)=57

x(1+50%)=60

x=40

Hence, The solution is, the number went in is 40.

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Answer:

b

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

y = 2x + 1 ← is in slope- intercept form

with slope m = 2

y = - [tex]\frac{1}{2}[/tex] x - 7 ← is in slope- intercept form

with slope m = - [tex]\frac{1}{2}[/tex]

• Parallel lines have equal slopes

the slopes are not equal thus not parallel

• the product of the slopes of perpendicular lines is equal to - 1

2 × - [tex]\frac{1}{2}[/tex] = - 1

Thus the 2 lines are perpendicular to each other.

This can be solved by Binomial Probability Distribution Method.

By solving we get P(B) = 0.25.

The binomial distribution is the discrete probability distribution used in probability theory and statistics that only allows for Success or Failure as the possible outcomes of an experiment. For instance, if we flip a coin, there are only two conceivable results: heads or tails, and if we take a test, there are only two possible outcomes: pass or fail. A binomial probability distribution is another name for this distribution.

P(X=x)=Cₙ.ₓ×p^x×(1-p)^(n-x)

Cₙ,ₓ=[tex]\frac{n!}{x!(n-x)!}[/tex]

The parameters are:

Case 1:

The coin is tossed 4 times, hence n=4

It is a fair coin, so it has equal number of chances for heads and tails. So P(a)=0.5

Case2:

P(B) is P(X=3),hence:

P(X=x)=Cₙ.ₓ×p^x×(1-p)^(n-x)

⇒P(X=3)=C₄,₃×(0.5)^3×(0.5)^(1)

⇒P(X=3)=0.25

This can be solved by Binomial Probability Distribution Method.

By solving we get P(B) = 0.25.

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This can be solved by Binomial Probability Distribution Method.

By solving we get P(B) = 0.25.

The binomial distribution is the discrete probability distribution used in probability theory and statistics that only allows for Success or Failure as the possible outcomes of an experiment. For instance, if we flip a coin, there are only two conceivable results: heads or tails, and if we take a test, there are only two possible outcomes: pass or fail. A binomial probability distribution is another name for this distribution.

P(X=x)=Cₙ.ₓ×p^x×(1-p)^(n-x)

Cₙ,ₓ= [tex]\frac{n!}{x!(n-x)!}[/tex]

The parameters are:

• x is the number of successes.

• n is the number of trials.

• p is the probability of a success on a single trial.

Case 1:

The coin is tossed 4 times, hence n=4

It is a fair coin, so it has equal number of chances for heads and tails. So P(a)=0.5

Case2:

P(B) is P(X=3),hence:

P(X=x)=Cₙ.ₓ×p^x×(1-p)^(n-x)

⇒P(X=3)=C₄,₃×(0.5)^3×(0.5)^(1)

⇒P(X=3)=0.25

This can be solved by Binomial Probability Distribution Method.

By solving we get P(B) = 0.25.

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Each type of coin marquis have is 18

The value of a dime is ten cents. The value of a quarter is 25 cents. Dimes are smaller than quarters. Fun fact: Copper and nickel, the metal used to create quarters and dimes, are the same. One dime is equal to ten cents. The value of a penny, often known as a one-cent coin, is one cent.

A dime coin is equivalent to 10 one-cent coins in value (pennies). The word "dime" derives from the Latin word "decimus," which means "one tenth." When they came up with the concept of money being split into ten parts in the 1500s, the French adopted the word "disme." The spelling was altered from "disme" to "dime" in America.

Here  d  =  number of dimes

Here  q  =  number of quarters and

Number equation:  d + q  =  26

Value equation:  0.10d + 0.25q  =  3.80

Here the value for the equation is multiplied by 100:  10d + 25q  = 380

the two equations:

d + q  +  26   --->   multipling by -10   --->    -10d - 10q  =  -260

10d + 25q  =  380                                --->   10d + 25q  = 380

Adding the columns:                                   15q  =  120

                                                                            q = 120/15

                                                                            q  =  8

                                                                             d + q  =  26

                                                                             d+8=26 ;        

                                                                             d=26-8    

                                                                              d  =  18

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The function f is continuous on (-∞, ∞).

A function f is said to be continuous at a point 'a' if,

lim ₓ→a f(x) = f(a).

f(x) = [tex]\left \{ {{1-x^2 if x\leq 1} \atop {ln x if x > 1}} \right.[/tex]

That is, if x ≤ 1, f(x) = 1 - x² and if x > 1, f(x) = ㏑ x

Taking interval (-∞, 1], f(x) is a polynomial 1 - x².

Polynomials are continuous everywhere. So f is continuous at (-∞, 1].

Now take the interval (1, ∞).

[tex]\lim_{x \to \infty} f(x)[/tex] = [tex]\lim_{x \to \infty} lnx[/tex] = ㏑ ∞ = ∞ = f(∞)

So f is continuous at the interval (1, ∞)

To check for continuity at 1,

lim x → 1⁻ f(x) = lim x → 1⁻ [1 - x²] = 1 - 1² = 0

lim x → 1⁺ f(x) = lim x → 1⁺ ㏑ x = ㏑ 1 = 0

So, lim x → 1⁻ f(x) = lim x → 1⁺ f(x)

So f is continuous in the whole interval (-∞, ∞).

Hence the function f(x) = [tex]\left \{ {{1-x^2 if x\leq 1} \atop {ln x if x > 1}} \right.[/tex] is continuous on the interval  (-∞, ∞).

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Answer:8

Step-by-step explanation:

Probability of Number of outcome is an even in likely situation is given as 512

Given that;

Number of time die roll = 1,000

Find:

Probability of Number of outcome is an even

Computation:

Probability of an even = 3 / 6

Probability of an even = 1 / 2

Probability of Number of outcome is an even = [Probability of an even]1000

Probability of Number of outcome is an even = [1/2]1000

Probability of Number of outcome is an even = 500

So most likely outcome is 512

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Answer:

Step-by-step explanation:

Formula for Circumference of a circle is 2* pi * radius

If r=16

C= 2*π*16

C=32π

Step-by-step explanation:

the factors are x-2+sqrt(3) and x-2- sqrt(3)

the basic form of the quadratic is x^2-4x+1, multiplying those factors together (there are 9 terms)

y=a(x^2-4x+1) is the general form

-2=a(-2)

a=1

a=(2/11)

the equation is y=x^2-4x+1

The recurrence relation for the number of bit sequences of length n with an even number of 0s is 2 [tex]a_{n-1}[/tex] for n>=2 and a1=1.

Let a be the even number of 0s in all the bit sequences of length n.

1st instance. The sequence begins with a 1, and there are [tex]a_{n-1}[/tex] such strings of length n-1 that must contain an even number of 0s.

Second instance. The sequence must begin with a 0, followed by an odd number of 0s in the subsequent n-1-length sequence. An even number of 0s can be found in one of the [tex]2^{n-1}[/tex] possible bit strings, so [tex]2^{n-1} -a_{n}[/tex] strings have an odd number of 0s.

[tex]a_{n}= a_{n-1}+2^{n-1} -a_{n-1}\\a_{n}=2^{n-1}[/tex]

Therefore, the recurrence relation is

an = 2[tex]a_{n-1}[/tex] for n >= 2.

a1 = 1.

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The correction made by the student is incorrect simplification of 30ab√2a+20a√2a

The perimeter of a polygon is the sum of its, all the side lengths.

Given that, the dimension of a rectangle is given by, √50a³b² and √200a³

The perimeter of the rectangle is = 2(length + width)

Solving for the perimeter,

2(√50a³b²+√200a³)

= 2(5ab√2a+10a√2a)

= 10ab√2a+20a√2a

The student solved it as 30ab√2a,

Which is incorrect, because 'b' is not there in both the expressions, hence, we cannot add them.

Hence, The correction made by the student is incorrect simplification of 30ab√2a+20a√2a

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Answer:

Step-by-step explanation:

Answer is D on Edge,

The student incorrectly simplified 10ab sqrt 2a + 20a sqrt 2a

The like radicals are 3x√x²y, –12x√x²y, x√yx² and 2√x²y.

A radical expression is an expression containing a square root.

Given are some expressions,

Like radicals are those whose entities in the square root are the same.

So, from the given options, like radicals are:

3x√x²y = This is like radical with the entity x²y  inside the square root.

–12x√x²y = This is like radical with the entity x²y  inside the square root.

x√yx² = This is like radical with the entity x²y  inside the square root.

2√x²y = This is like radical with the entity x²y  inside the square root.

Hence, The like radicals are 3x√x²y, –12x√x²y, x√yx² and 2√x²y.

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Answer:

We can solve this problem by using the information provided in the riddle to create a system of equations. Let x be the number of pencils that were originally in the box. We can then create the following equations:

x < 40

x - 4 = 2

x - 3 = 0

x - 5 = 0

We can then solve this system of equations to find the value of x. First, we note that the second and third equations imply that x is equal to 3 or 5. Substituting these values into the first equation, we find that x cannot be 3, as this would violate the inequality. However, x can be 5, as 5 is less than 40. Therefore, the number of pencils that were originally in the box is 5.

The inequality or number of units produced per hour is 15.50<10+0.50x.

Mathematical expressions with inequalities are those in which the two sides are not equal. Contrary to equations, we compare two values in inequality. Less than (or less than or equal to), greater than (or greater than or equal to), or not equal to signs are used in place of the equal sign.

Given:

According to the question the inequality can be

15.50<10+0.50x

15.50-10<0.50x

5.50<0.50x

5.50/0.50x

x> 11

For checking the Inequality

Let x=12.

15.50<10+.50*12

15.50+10+6

15.50<16

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This means that in order to make at least $790, the drama club must sell 47 number of student tickets. 47,48,49,50,51

The first equation is 5x + 7(73) = 790, where x is the number of student tickets. We can solve this equation to determine that x = 47. This means that in order to make at least $790, the drama club must sell 47 student tickets. Then, we can check the other possible values of x to see how many tickets they must sell. The other possible values are 48, 49, 50, and 51. Therefore, the answer is 47, 48, 49, 50, 51.

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Answer:

The dimensions of the right triangle are 9 meters by 7 meters.
or
The base of the triangle is 9 meters, and the height is 7 meters (since the height is 2 meters less than the base).

Step-by-step explanation:

To find the dimensions of the right triangle, we can use the formula for the area of a triangle, which is:

A = 1/2 * b * h

Where b is the base and h is the height of the triangle. In this case, we know that the area of the triangle is 40 square meters, and the height is 2 meters less than the base, so we can write the equation as:

40 = 1/2 * b * (b - 2)

To solve for b, we can rearrange the equation to get b by itself:

40 = 1/2 * b^2 - b

Then, we can move all the terms involving b to the left-hand side of the equation and all the constants to the right-hand side:

1/2 * b^2 - b - 40 = 0

Next, we can use the quadratic formula to solve for b:

b = (-(-1) +/- sqrt((-1)^2 - 4 * (1/2) * -40)) / (2 * (1/2))

Which simplifies to:

b = (1 +/- sqrt(1 + 80)) / 1

Since b must be a positive number, we take the positive solution:

b = (1 + sqrt(81)) / 1

Therefore, the base of the triangle is 9 meters, and the height is 7 meters (since the height is 2 meters less than the base). Thus, the dimensions of the right triangle are 9 meters by 7 meters.

Answer:

Step-by-step explanation:

Use the form

a

cos

(

b

x

−

c

)

+

d

to find the amplitude, period, phase shift, and vertical shift.

Answer: 10

Step-by-step explanation:

10 times 10 = 100

So square root of 100 = 10

An expression that finds Enzo's net worth is:

$ 127100 - $ 88500.

What is the net worth?

The amount by which the value of the assets exceeds the liabilities is the net worth (equity) of the business. The net worth reflects the amount of ownership of the business by the owners. The formula for computing net worth is. Assets - Liabilities = Net Worth.

Enzo's net worth is the difference between the amount of money he has and the amount of money he owes. Therefore, the correct expression is: 88,500 dollars minus 127,100 dollars.

net worth = Assets - liabilities

net worth = 127100 - 88500

net worth = 38600.

This expression would give us the difference between the two amounts, which is the net worth.

The other expressions are not correct because they do not represent the difference between the two amounts.

127,100 dollars minus 88,500 dollars would give us the difference between the two amounts, but this difference would be the opposite of the net worth.

127,100 dollars divided by 88,500 dollars would give us the ratio of the two amounts, which is not the same as the net worth.

88,500 dollars is just the amount of money that Enzo has, and it does not take into account the amount of money he owes.

127,100 dollars is just the amount of money that Enzo owes, and it does not take into account the amount of money he has.

Hence, An expression that finds Enzo's net worth is:

$ 127100 - $ 88500

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Solid chance this is way above your knowledge level



A parabola is a curve in the shape of a U that is defined as the set of all points that are equidistant to a fixed point (called the focus) and a fixed line (called the directrix).

To write the equation of a parabola with a focus at (-2, 5) and a directrix at x = 3, we can use the standard form of the equation of a parabola, which is:

y = (1/(4f))x^2 + k

Where f is the distance between the focus and the vertex (the point where the parabola changes direction), and k is a constant that determines the position of the parabola along the y-axis.

To find the value of f, we can use the distance formula:

f = sqrt((x2 - x1)^2 + (y2 - y1)^2)

Where (x1, y1) is the coordinate of the focus and (x2, y2) is the coordinate of the vertex.

Since the focus is at (-2, 5) and the directrix is at x = 3, we can use the y-coordinate of the focus as the y-coordinate of the vertex, and the x-coordinate of the directrix as the x-coordinate of the vertex. Therefore, the coordinate of the vertex is (3, 5).

Substituting these values into the distance formula, we get:

f = sqrt((3 - (-2))^2 + (5 - 5)^2)

= sqrt((5)^2 + (0)^2)

= sqrt(25)

= 5

Now that we have the value of f, we can substitute it into the standard form of the equation of a parabola to get:

y = (1/(4*5))x^2 + k

= (1/20)x^2 + k

This is the equation for a parabola with a focus at (-2, 5) and a directrix at x = 3. The constant k determines the position of the parabola along the y-axis.

Answer:

Use desmos to help with slopes and finished equations its a graphing calculator and its very helpful

Step-by-step explanation:

Answer:

y=3x-8

Step-by-step explanation:

slope, or m (3), is always next to an x. y-intercept (-8) goes always after the mx

The area enclosed by the curve x = t2 − 3t, y = t and the y-axis is 9/2

In this question we have been given parametric equations x = t^2 − 3t, y = t

In this question we need to find the area enclosed by the curve x = t2 − 3t, y = t and the y-axis.

The curve has intersects with y-axis.

Consider x = 0

So, t^2 − 3t =  0

t(t - 3) = 0

t = 0   or  t = 3

Let f(t) =  t^2 − 3t and g(t) = t

Now we have to draw the graph,

Differentiate the curve f(t) with respect to t.

f'(t) = 2t - 3

Now, find the area under the curve using the above formula

A = ∫[a to b] g(t)f'(t) dt

so, A = ∫[0 to 3] t (2t - 3) dt

A = ∫[0 to 3] (2t^2 - 3t) dt

A = [2/3 t^3 - 3/2 t^2]_[t = 0, t = 3]

A = 2/3 3^3 - 3/2 3^2

A = 18 - (3^3)/2

A = 18 - 27/2

A = 9/2

Therefore,  the area of the curve is 9/2.

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Answer:

Step-by-step explanation:

Your second option is your answer;

Arrow pointing to the right with circle filled. Your arrow would start at the 2.

The perfect square trinomial in y = ( [tex]x^{2} + 2x + 1[/tex] ) -1 - 1 will be

⇒ [tex](x+1)^{2}[/tex]

The perfect square trinomial in y = (x + 2)2 - 1 - 1 will be

⇒ Null

A perfect square trinomial can be expressed as the square of a binomial,

We can write the first expression as,

y = [tex]x^{2} + 2x + 1[/tex]

y = [tex]x^{2} + 2x + 1 - 2[/tex]

⇒ [tex]x^{2} + x + x + 1[/tex]

⇒ [tex]x(x + 1) + 1(x + 1)[/tex]

⇒ (x + 1) (x + 1)

⇒ [tex](x + 1)^{2}[/tex]

Therefore, according to the first expression, [tex](x^{2} + 2x + 1) -1 - 1[/tex] is a perfect square binomial with the factor = [tex](x + 1)^{2}[/tex]

According to the second expression, y = (x +2)2 − 1 −1

This expression does not show any factors

Therefore, this second expression doesn't have any perfect square trinomial factors.

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Factor the perfect-square trinomial in y = (x2 + 2x + 1) − 1− 1, y = (x +2)2 − 1 −1

Answer: 1

Step-by-step explanation:

got it right