Write a polyomial equation of degree 4 that has the following roots: -1 repeated three times and 4.

Using the combination formula, it is found that:

There are 364 different orders of top-three finishers that include all seniors.

The probability that the top-three finishers will all be seniors is 15.38%.

The order in which the players are taken is not important, hence the combination formula is used to solve this question.

[tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by:

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

In total, three students are taken from a set of 14, hence:

[tex]C_{14,3} = \frac{14!}{3!11!} = 364[/tex]

Including only seniors, it would be three students from a set of 8, hence:

[tex]C_{8,3} = \frac{8!}{3!5!} = 56[/tex]

Hence the probability is given by:

p = 56/364 = 0.1538 = 15.38%.

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Applying the inscribed angle theorem, the measure of arc AB that doesn't go through point C is: 100 degrees.

Based on the inscribed angle theorem, if ∅ is the inscribed angle measure, the measure of the central angle subtended by the same arc equals 2(∅).

m∠BAC = 40 degrees.

Central angle = 2(40) = 80 degrees [based on the inscribed angle theorem]

Corresponding arc BC = 80 degrees.

Arc AC through point B = 180 degrees [half circle]

Arc AB = 180 - arc BC = 180 - 80 = 100 degrees.

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The simplified value is shown below:

Exponent refers to the number of times a number is used in a multiplication. Power can be defined as a number being multiplied by itself a specific number of times.

First,

3²*4³*[tex]2^{-1}[/tex]/(3*4)²

=9*64/144*2

= 576/288

=2

Second,

(3*2)^4 *[tex]3^{-3}[/tex]/2³*3

=1296/8*81

=1296/648

=2

Third,

[tex]3^{-3} *2^{-3} *6^{3} /(4^{0} )^{2}[/tex]

= [tex]6^{3} /(1 )^{2} *3^{3} *2^{3}[/tex]

= [tex]2^{3}* 3^{3} /(1 )^{2} *3^{3} *2^{3}[/tex]

=1

Fourth,

[tex]2^{4}* 3^{5} /(2*3)^{5}\\=2^{4}* 3^{5} /2^{5}*3^{5}[/tex]

= 1/2

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Answer:

In the first step, there is an issue when distributing the -3 to the terms inside of the parentheses. When multiplying the -3 to the -5, you would get an answer of +15, not -15.

The full correct process is:

(4m + 9) - 3(2m - 5) = 4m + 9 - 6m + 15

                                = 4m - 6m + 9 + 15

                                = -2m + 24

Answer:

A. median

explain i just aced the test rn

Answer:

Angle bisector

Step-by-step explanation:

The line AD bisects both sides of the triangle. Both angles are congruent to each other since both sides are congruent to each other.

For the given function, the domain is D : { x ≥ 7} and the range is R: { y ≥ 9}

Here we have a square root, remember that the argument of the square root must be equal or larger than zero, so the domain is such that:

x - 7 ≥ 0.

Solving for x we get:

x ≥ 0 + 7

Then the domain is:

x ≥ 7

To get the range, we evaluate in the minimum of the domain:

f(7) = √(7 - 7) + 9 = 9

Then the range is the set of all values larger than 9, because the function is increasing.

So the range is R: y ≥ 9.

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The system of equations have one solution

The equations are given as:

2x + 2y = 5

3x + 3y = 7

The above equations are distinct linear equations.

This means that they would have one point of intersection, if plotted on a graph

Hence, the system of equations have one solution

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Answer:

Molly's jump rope is 1 2/3 feet longer than Gail's jump rope.

Step-by-step explanation:

To get this answer, you would have to subtract 6 1/3 - 4 2/3 to find the difference between the two lengths.

To solve this subtraction problem: Start by doing 6 - 4 to get 2, because when the fraction parts are like that, start with whole numbers. Then, solve the fraction parts. 1/3 - 2/3 is -1/3 (you can go to negatives)! Lastly, combine the whole number and fraction parts. 2 - 1/3, because the negative symbol changes to a minus symbol, which will get you 1 2/3.

Hope this helped!

Answer:

The first step for deriving the quadratic formula from the quadratic equation, 0 = ax2 + bx + c, is shown.

[tex] \: first the formula of quadratic equation \: = - b ≠ \: \sqrt{ \frac{ \: {b }^{2} - 4ac}{ \: 2a} } [/tex]

let's begin to solve this equation,,,

[tex]ax² + bx + c = 0 \\

ax² + bx + c =0 \\ {x}^{2} + \frac{b}{a} \: + \frac{ {b}^{2} }{2a} = \frac{b2}{a} - \frac{c}{a}

\\ x + \frac{ {b}^{2} }{2a} = - \frac{ {b}^{2} }{2a} - \frac{c}{a} [/tex]

an equation having the maximum power of the variable equal to is called the quadratic equation the general form of quadratic equation is ax² + bx +c =0 where a,b,c are real numbers a ≠0 x is variable •

a quadratic equation can be solved by two method by factorization and by formula

by factorization a quadratic equation can be solved by factorization only when the product AC can be divided into two such part that it had the sum of the difference of the two part is equal to b

[tex]by the formula of quadratic equation can be solved by \ - } [/tex]

[tex]x = \frac{ - b \sqrt{ {b}^{2} - 4ac } }{2a } \\ root \: of \: equation \: {ax}^{2} + bx + c = 0 \\ - b - \sqrt{ \frac{ {b}^{2} - 4ac}{2a} } [/tex]

The answer will be x squared over 4 plus y squared over 8 equals 1.

An ellipse is an oval shape geometry having two focuses and the curve is equidistant from the focus.

The general equation of the ellipse is given as;

(x²/a²) + (y²/b²) = 1

The coordinates of a foci are: (±c, 0) where;

c² = b² - a²

However, we know that equation of directrix is; x = ±a/e

Now, Directrix is given ±4

Thus, a/e = 4

a = 4e

We also know that c = ae from ellipse foci coordinates.

Thus, ae = 2

since ae = 2, then (4e)e = 2

4e² = 2

e² = 2/4

e = 1/2

Thus;

a = 4 × 1/2

a = 2

Since c² = b² - a²;

2² = b² - 2²

4 = b² - 4

b² = 8

From (x²/a²) + (y²/b²) = 1, we can put our values to get;

x²/4 + y²/8 = 1

Hence the answer will be x squared over 4 plus y squared over 8 equals 1.

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The probability that the student selected at random is a freshman is; 29%

From the given table;

Total number of male students = 4 + 6 + 2 + 2 = 14

Number of freshmen students = 4 students

Thus;

Probability that the student selected at random is a freshman is;

P(Freshman | Male) = 4/14 * 100% = 28.57% ≈ 29%

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The distribution of the values obtained from a simple random sample of size n from the same population is incorrect.

The sampling distribution of a statistic of size n is the distribution of the values obtained from a simple random sample of size n from the same population.

The sampling distribution is the process of getting a sample through simple random techniques from the sample population.

So, it is incorrect that the distribution of all values of the statistic when all possible samples of the same size n are taken from the same population.

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The probability that sample the proportion of adults with hypertension is greater than 0.5 is 0.090

The given parameters are:

p = 47%

Sample size, n =500

The standard deviation is calculated as:

[tex]\sigma = \sqrt{np(1 - p)[/tex]

So, we have:

[tex]\sigma = \sqrt{500 * 47\%(1 - 47\%)[/tex]

Evaluate

σ = 11.16

The number of adults with hypertension is calculated as:

x = 500 * 0.5 = 250

And the mean is:

μ = 500 * 0.47 = 235

Start by calculating the z-score

[tex]z = \frac{x - \mu}{\sigma}[/tex]

This gives

[tex]z = \frac{250 - 235}{11.16}[/tex]

Evaluate

z = 1.34

The probability is then calculated as:

P(z >1.34) = ??

From z table of probabilities, we have:

P(z >1.34) =  0.090

Hence, the probability that sample the proportion of adults with hypertension is greater than 0.5 is 0.090

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By quadratic formula, the roots of the quadratic function 2 · x² - 2 · x + 5 = 0 are two conjugated complex numbers: x₁ = 0.5 + i 1.5 and x₂ = 0.5 - i 1.5, respectively.

Let be a quadratic function of the form a · x² + b · x + c = 0, whose roots can be found by means of the following formula:

[tex]x = \frac{-b \pm \sqrt{b^{2}-4\cdot a\cdot c}}{2\cdot a}[/tex]     (1)

Where a, b, c are the coefficients of the quadratic function.

In we know that 2 · x² - 2 · x + 5 = 0, then the roots of the polynomial are, respectively:

[tex]x_{1} = \frac{2 + \sqrt{(-2)^{2}-4\cdot (2)\cdot (5)}}{2\cdot (2)}[/tex]

[tex]x_{1} = \frac{2 + \sqrt{4-40}}{4}[/tex]

x₁ = 0.5 + i 1.5

[tex]x_{2} = \frac{2 - \sqrt{(-2)^{2}-4\cdot (2)\cdot (5)}}{2\cdot (2)}[/tex]

[tex]x_{2} = \frac{2 - \sqrt{4-40}}{4}[/tex]

x₂ = 0.5 - i 1.5

By quadratic formula, the roots of the quadratic function 2 · x² - 2 · x + 5 = 0 are two conjugated complex numbers: x₁ = 0.5 + i 1.5 and x₂ = 0.5 - i 1.5, respectively.

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The independent variable: number of pounds of fertilizer; and dependent variable: number of square feet of garden covered.

Let

Dependent variable are variables which takes its value based on other values in an equation.

Independent variable are variables which takes its value outside an equation.

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Based on the calculations, the first three (3) iterations of the given function are 120, 96 and 76.8.

In this exercise, you're required to find the first three (3) iterations of the given function. Thus, we would substitute the value of x₀ into the function and then evaluate as follows:

First iteration:

f(x) = 0.80x

f(x₀) = 0.80x₀

f(150) = 0.80 × 150

f(150) = 120.

Second iteration:

f(x) = 0.80x

f(x₁) = 0.80x₁

f(120) = 0.80 × 120

f(120) = 96.

Third iteration:

f(x) = 0.80x

f(x₂) = 0.80x₂

f(96) = 0.80 × 96

f(120) = 76.8.

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Answer:

45m

Step-by-step explanation:

4m+19m+14m+8m=45m

Answer:

My guess would be b or d

Step-by-step explanation:

Answer: The correct answers are the first and the fourth one.

Step-by-step explanation:

A triangle is a three-edged polygon with three vertices. If the triangle is rotated 180° about the cross then it will be done as shown below.

A triangle is a three-edged polygon with three vertices. It is a fundamental form in geometry. The sum of all the angles of a triangle is always equal to b

If the triangle is rotated 180° about the cross then it will be done as shown below. This is because the triangle is 2 units away from the cross(dot) therefore, after rotation it will be at the same distance from the point.

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[tex]~~~~~~k = \dfrac{3n+2}{n+1}\\\\\implies k(n+1) = 3n+2\\\\\implies kn+k=3n+2\\\\\implies kn -3n= 2-k\\\\\implies n(k-3) = 2-k\\\\\implies n = \dfrac{2-k}{k-3}\\\\\implies n = -\dfrac{k-2}{k-3}~~~~~~~~;[k\neq 3][/tex]

Answer:

119 4/7

Step-by-step explanation:

Add up all the sides

Hi Student!

Looking at the picture that was provided, we see that the problem statement is asking for us to determine the perimeter of the shape is.  Perimeter is the outer layer of the shape which would include the lengths of all the sides that are exposed to the outside.

In this case, we are given 7 different values which represent each of the different sides of the shape which we need to add together to get the perimeter.

Create an expression

Using the expression above, all we need to do is combine all of the values which will give us the outline on our shape.  However, since some of the values have different denominators, we will first need to combine the whole numbers and then combine those with a common denominator and finally apply a common denominator to be able to add the rest.

Combine the whole numbers

Combine those with a common denominator

Covert to mixed fraction and simplify

Find common denominator and combine

Simplify the expression

Therefore, the final answer for the perimeter of the figure that was provided would be [tex]119\frac{4}{7}[/tex] units.

Answer:

y = 7x +2

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 )

calculate m using the slope formula

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

with (x₁, y₁ ) = (0, 2 ) and (x₂, y₂ ) = (- 1, - 5 )

m = [tex]\frac{-5-2}{-1-0}[/tex] = [tex]\frac{-7}{-1}[/tex] = 7

the line crosses the y- axis at (0, 2 ) ⇒ c = 2

y = 7x + 2 ← equation of line

Answer:

2.5 cups is equal to 1 pound.

Step-by-step explanation:

___2.5__ cups rice is equivalent to 1 pound

Hope This Helped

Answer:

2.5 cups of rice

I hope this helps

The exponential function of the table is y = 0.75(2)^x

From the table, we have the following points

(x,y) = (0,0.75) and (1,1.5)

An exponential function is represented as:

y = ab^x

At (0,0.75), we have:

0.75 = ab^0

a = 0.75

Substitute a = 0.75 in y = ab^x

y = 0.75b^x

At (1,1.5), we have:

1.5 = 0.75b^1

Evaluate

1.5 = 0.75b

Divide both sides by 0.75

b =2

Substitute b =2 in y = 0.75b^x

y = 0.75(2)^x

Hence, the exponential function is y = 0.75(2)^x

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Answer:

-3y+8z

Step-by-step explanation:

2x-2y+5z-2x-y+3z

you don't need to change their signs just place them accordingly

2x-2x-2y-y+5z+3z

-3y+8z