Write the linear equation for the graph of line q.

y = x+

The total zeros the function has is 4

See below for other solutions

This is the degree of the function

The degree of f(x) = -x^4 + x^3 - 7x2 + 9x + 18 is 4

So, the number of zeros is 4

Start by writing out the factors of the leading coefficient and the constant term

p = ±(1, 2, 3, 6)

q = ±1

So, we have

p/q = ±(1, 2, 3, 6)/±1

p/q = ±(1, 2, 3, 6)

Here, we find the number of changes in sign in the coefficients of the polynomial function.

f(x) = -x^4 + x^3 - 7x2 + 9x + 18

Number of sign changes = 3

Calculate f(-x) for the negative zeros

f(-x) = -(-x)^4 + (-x)^3 - 7(-x)^2 + 9(-x) + 18

f(-x) = -x^4 - x^3 - 7x^2 - 9x + 18

Number of sign changes = 1

This means that there is the possibility of 3 positive zeros, 1 negative zero, and 1 complex zero.

Here, we make use of the leading term, -x4, which is negative.

This implies that the graph will approace -∝ as x approaches +∝ and will approach +∝ as x approaches -∝.

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The mean duration of the game will be 70%.

The likelihood of not receiving any color will be equal to the likelihood of receiving one fewer ball of each hue:

P(green) = 2/5 P(red after green) = 3/6

P(green after yellow after red) = 1/4 0.5 x 0.4 x 0.25 = 0.05

Suppose we follow a different order:

Yellow has the following probabilities: P(yellow) = 1/6, P(red after yellow) = 3/5, and P(green after red after yellow) = 2/4.

As you can see, we also get denominators of 4,5,6, and numerators of 1, 3, and 2!

Therefore, the result probably will be 0.05 for any feasible combination (believe me on this one)!

How many possible combinations exist?

RGY\sRYG\sYGR\sYRG\sGRY\sGYR

6 combinations are thus feasible. The likelihood of each at 0.05 times 6 equals 0.3.

6 combinations are thus feasible. The likelihood of each at 0.05 times 6 equals 0.3.

The likelihood of all outcomes minus the ones we discovered, or 1 - 0.3 = 0.7, is the probability of not receiving distinct colors.

So 70% is the answer.

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The degree and leading coefficient of each polynomial in one variable is given below :- (2). degree 3; leading coefficient 8 | (4). degree 6; leading coefficient | (6). not a polynomial

The "leading coefficient" is the coefficient of the highest-degree term in the sum of terms that makes up a polynomial.

These expressions all have one variable, so the number of variables is not an issue in any case. All of the exponents are positive integers, so that is not an issue in any case. However, the variable appears in the denominator in the expression of problem 6, so that sum is not a polynomial.

______

(2). In order to put this into the form we recognize as a polynomial, the expression must be "simplified' by performing the multiplication of the two factors:

= 8x³ -4x² +6x -3

The leading coefficient is the coefficient of the highest-degree term, which is the product of the highest-degree terms of the factors. That product is ...

 (2x)(4x²) = 8x³

so the leading coefficient is 8. The variable is to the 3rd power, so the degree is 3.

______

(4). The expression is already written as a sum, so we only need to find the term of highest degree. That is the last one: 7y^6. Its degree is 6 and its leading coefficient is 7.

_____

(6). Variables are not allowed in the denominator of a polynomial. This expression is not a polynomial.

Hence the degree and leading coefficient of each polynomial in one variable is given below :-

(2). degree 3; leading coefficient 8 | (4). degree 6; leading coefficient | (6). not a polynomial

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----------- Correct format of the question is given below --------

(Q). State the degree and leading coefficient of each polynomial in one variable. if it is not a polynomial in one variable, explain why?

*equations of each polynomial is given below in image.*

The exponential function that models the number of bacteria after x hours is given as follows:

y = 5(7)^x.

An exponential function is defined as follows:

y = a(b)^x.

In which the parameters are given as follows:

The initial amount of bacteria was of 5, hence the parameter a is obtained as follows:

a = 5.

After one hour, the number of bacteria was multiplied by 7, as 35/5 = 7, hence the parameter b is obtained as follows:

b = 7.

Thus the function is given as follows:

y = 5(7)^x.

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Answer:

No, the following ratios are not proportional, because they are not equal, nor can be reduced.

Step-by-step explanation:

Hope it helps! =D

Yes, the connection between the semimajor axis and an orbit's period varies as the eccentricity of the orbit changes.

In geometry, the eccentric definition is the distance from any point on a conic section to the focus divided by the perpendicular distance from that point to the nearest directrix. In general, eccentricity aids in determining the curvature of a form. The eccentricity grows as the curvature lowers.

Here,

In general, an orbit's period is proportional to the square root of the semimajor axis multiplied by three. This connection, however, is only valid for circular orbits with zero eccentricity. When the eccentricity is larger than zero, the period of the orbit is still determined by the magnitude of the semimajor axis, but it is also determined by the form of the orbit as given by the eccentricity. The relationship between the semimajor axis and the period in this situation is not as straightforward as a proportionate relationship.

As a result, modifying an orbit's eccentricity modifies the connection between the semimajor axis and the period.

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Answer:

(5, 42)

Step-by-step explanation:

22 + 4x= 42

There is only one that will work.

42 - 22 = 20

4x = 20

x= 5

"  X is the number of weeks they have gotten the allowance "

Answer: D. (5,42)

Step-by-step explanation:

If x is representing the weeks that she received her allowance, this means that we would need to add 4 to her starting amount (22) for every week.

So, if she got an allowance for 5 weeks, we would need to multiply her earning amount (4 per week) by the number of weeks (5).

5 x 4 = 20

But, we aren't done just yet! We still need to add this amount to her starting balance, which is $22. So, 20 + 22 = 42.

So, if x is 5, y would be 42, just like in the answer!

Another way of solving this answer would be 22 + 4x = 42.

I hope this helped you :)

Cheers!

different outcomes have at least heads 2048, 165, 2036, 1816,

1. total number of different outcomes for 11 times toss

=2048

2. exactly 8 heads can be found by combination ( exactly n heads possiblity can be found by 11Cn

= 165

3. number of outcomes with atleast 2 heads can be found by subtracting number of outcomes with with 0 and 1 heads from total number of outcomes

= total number of outcomes - outcomes with 0 heads - outcomes with 1 heads

= 2036

4. number of outcomes with atmost 7 heads can be found by subtracting number of outcomes with  8, 9, 10, 11 heads from total number of outcomes

= total number of outcomes - outcomes with 8 heads - outcomes with  9 heads - outcomes with  10 heads -outcomes with  11 heads

=1816

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If you divide $320 by 40 your answer is 8, so Mary probably earns 8 dollars an hour.

Answer:

C 2.04, 2.3, 2.36, 2.4

Step-by-step explanation:

Start comparing from left to right.

2.36

2.4

2.04

2.3

The ones digit has a 2. All numbers have a 2 in the ones digit, so so far they are all the same.

Now move over one digit to the right. It is the first digit to the right of the decimal point. It is the tenths digit. Compare the numbers in the tenths digit.

2.36

2.4

2.04

2.3

The tenths digit contains a 3, a 4, a 0, and a 3. Now put the numbers in increasing order by the tenths digit.

2.04

2.36

2.3

2.4

The digits in the tenths place are now in increasing order. Now we look at the next digit to the right, the hundredths digit. If a number has no digit in the hundredths place, put a zero there.

2.04

2.36

2.30

2.40

The only change we see that we need to make is the two middle numbers.

2.04

2.30

2.36

2.40

Answer: 2.04, 2.30, 2.36, 2.40

The image of △ABC is the triangle with vertices (-1, -6), (1, -2) and (3, -2)

The image of point (x,y) after reflecting across the x-axis is (x, -y) and after the translation it is (x + 4, -y).

Applying these transformations to each vertex of △ABC:

So, the image of △ABC is the triangle with vertices:

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Therefore , the solution of the given problem of unitary method  comes out to be total cost for to make 15 jars is  12,386.25 euroes.

After calculating the size of a small slice, multiply the quantity by two to complete a task using the unitary technique. Simply expression, the unit variable technique works to separate a coded item from a certain group or collection of groups. For instance, 40 pens would cost Rs. 400 (or 400 pounds, $1.01). It's possible that one country will have total control over the method employed to do this. Almost every living creature has a distinctive quality.

Here,

Given :

cost of blackberry = 88 euroes

cost of sugar = 650 euroes

Jam bottles costs =87.75

total cost for to make 15 jars is

=> 15 * (87.75+650+88)

=> 15 * 825.75

=>  12,386.25 euroes

Therefore , the solution of the given problem of unitary method  comes out to be total cost for to make 15 jars is  12,386.25 euroes.

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I runner is running at the speed of 6.8 miles/hr and he wants to run 10.1 km then he runner must run for 9.3 minutes.

To calculate this, we first need to convert the given speed from miles per hour to kilometers per hour. 6.8 mi/hr is equal to 10.9 km/hr.

Then, we need to divide the total distance (10.1 km) by the speed (10.9 km/hr) to get the total time it will take for the runner to complete the 10.1 km run.

10.1 km/10.9 km/hr = 0.922 hr = 9.3 minutes.

Therefore, the runner must run for 9.3 minutes in order to complete the 10.1 km run.
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The equations that can verify the solution.

-48 = -35 - 13

-48 = 7(-5) - 13

-48 = -7(5) - 13

Options B, C, and D are the correct answer.

An equation is a mathematical statement that is made up of two expressions connected by an equal sign.

Example:

2x + 3 = 6 is an equation.

We have,

-48 = -7x P - 13

-48 + 13 = -7P

-35 = -7P

P = 5

The solution is 5.

This means,

-48 = - 7 x 5 - 13

-48 = -35 - 13

-48 = -48

Verified.

Now,

A.

-48 = -7(-5) - 13

-48 = 35 - 13

-48 = 22

Not true.

B.

-48 = -35 - 13

-48 = -48

Verified.

C.

-48 = 7(-5) - 13

-48 = -35 - 13

-48 = -48

Verified.

D.

-48 = -7(5) - 13

-48 = -35 - 13

-48 = -48

Verified.

E.

48 = 35 + 13

48 = 48

True.

F.

48 = 7(5) + 13

48 = 35 + 13

48 = 48

True.

Thus,

-48 = -35 - 13

-48 = 7(-5) - 13

-48 = -7(5) - 13 equations can verify the solution.

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Suppose a system of equations has 3 equations and 5 variables. additionally, suppose the coefficient matrix for the system has 3 pivot columns. Based on the information provided, it is consistent.

The number of pivot columns in the coefficient matrix of a system of equations determines the rank of the matrix, which is a measure of the number of linearly independent rows or columns. A system of equations is consistent if and only if the rank of the coefficient matrix is equal to the number of unknowns in the system.

In this case, the system has 3 equations and 5 variables, so it is not immediately clear if the rank of the coefficient matrix is equal to the number of unknowns. Additionally, the number of pivot columns alone is not enough to determine the consistency of the system, as there may be additional relationships between the variables that affect the rank.

So,  Based on the information provided, it is consistent.

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The amount that Riley paid for the hair dryer is $225.37.

Given the information in the question, the dryer is depreciating in value. Depreciation is when the value of an asset declines with the passage of time.

The formula that can be used to determine the amount paid for the hair dryer is:

p = FV / (1 - r)^n

Where:

p = $100 / (1 - 0.15)^5

p = $100 / 0.85^5

p = $225.37

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the answer is in the picture.. if you have any questions feel free to ask

If we consider all possible mixed strategies for player 2, then the number of strategies that player 2 has is infinite.

In the extensive-form game provided, player 2 has two decision points where they can choose between two actions, C and F in the first decision point and G and not-G in the second decision point. Therefore, player 2 has 2 x 2 = 4 pure strategies.

However, player 2 can also mix their strategies in each decision point, choosing a probability distribution over the available actions. For example, in the first decision point, player 2 can play a mixed strategy where they choose C with some probability and F with the complementary probability. Similarly, in the second decision point, player 2 can mix their strategies by choosing to play G with some probability and not-G with the complementary probability.

So, if we consider all possible mixed strategies for player 2, then the number of strategies that player 2 has is infinite.

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In the extensive-form game that follows, how many strategies does player 2 have?

[tex]\huge\begin{array}{ccc}f(x)=\dfrac{4}{5}x-5\end{array}[/tex]

We have:

[tex]f(5)=-1\\\\f(0)=-5[/tex]

therefore we have two points on the line:

[tex](5,-1),\ (0,-5)[/tex]

Use the two points-slope formula:

[tex]A(x_a,\ y_A),\ B(x_B,\ y_B)\\\\y-y_A=\dfrac{y_B-y_A}{x_B-x_A}(x-x_A)[/tex]

Substitute:

[tex](5,-1)\to x_A=5,\ y_A=-1\\(0,-5)\to x_B=0,\ y_B=-5[/tex]

[tex]y-(-1)=\dfrac{-5-(-1)}{0-5}(x-5)\\\\y+1=\dfrac{-5+1}{-5}(x-5)\\\\y+1=\dfrac{-4}{-5}(x-5)\\\\y+1=\dfrac{4}{5}(x-5)\\\\y+1=\dfrac{4}{5}x-4\\\\y+1-1=\dfrac{4}{5}x-4-1\\\\\boxed{y=\dfrac{4}{5}x-5}[/tex]

Answer:

f(x) = 0.8x - 5

Step-by-step explanation:

the equation of a linear function is of the form

f(x) = ax + b

to find  a and b use the given points

f(5) = - 1 ⇒ (5, - 1)

f(0) = - 5 ⇒ (0, - 5 )

substituting into the standard form , (0, - 5 )

- 5 = a(0) + b

- 5 = b

then

f(x) = ax - 5

substitute the other point (5, - 1 )

- 1 = 5a - 5 ( add 5 to both sides )

4 = 5a ( divide both sides by 5 )

[tex]\frac{4}{5}[/tex] = a

f(x) = [tex]\frac{4}{5}[/tex] x - 5

or

f(x) = 0.8x - 5

If the data has a mound-shaped distribution, then percentage of dentists who use less than 102 units of local anesthetics per week is  84%   .

The Distribution is mound shaped and symmetric

we have to find percentage of dentists use less than 102 units of local anesthetics per week ;

Since the distribution is mount shaped , 68% of the data values are within 1 standard deviations of the mean (by the empirical rule) and 32% of data values are more than 1 standard deviations (23) from mean (79) .

Since , Distributions is symmetric, we expect about 16% of the data values to be more than 1 standard deviations below the mean, and about 16% of data values to be more than 1 standard deviations above mean.

So , 68% + 16% = 84% of the data values is expected to be less than 102.

Therefore , 84% of dentists use less than 102 units of local anesthetics per week .

The given question is incomplete , the complete question is

A study published in Current Allergy & Clinical Immunology (Mar. 2004) investigated allergic reactions of dental patients to local anesthetics. Based on a survey of dental practitioners, the study reported that the mean number of units (ampoules) of local anesthetics used per week by dentists was 79, with a standard deviation of 23. Suppose we want to determine the percentage of dentists who use less than 102 units of local anesthetics per week.

Assuming that the data has a mound-shaped distribution, what percentage of dentists use less than 102 units of local anesthetics per week ?

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[tex]~~~~~~ \textit{Continuously Compounding Interest Earned Amount} \\\\ A=Pe^{rt}\qquad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill & \$3000\\ r=rate\to 6\%\to \frac{6}{100}\dotfill &0.06\\ t=years\dotfill &2 \end{cases} \\\\\\ A = 3000e^{0.06\cdot 2} \implies A \approx 3382.49~\hfill \underset{interest~only}{\stackrel{3382.49~~ - ~~3000}{\approx\text{\LARGE 382.49}}}[/tex]

TLDR: 88%

The probability of neither event happening is the complement of the probability of either event happening, which is 100 - 12 = 88.

Cheers,

qxxi

The solutions for the infinite solutions have the same set of coefficients on both sides of the equations

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the first equation be represented as A

Now , the value of A be

ax + by = 0

Let the second equation be represented as B

Now , the value of B be

cx + dy = 0

For the system of equations to have infinite solutions , the coefficients of both the equations should be same

So , when a = c and b = d

ax + by = cx + dy

Hence , when the coefficients of the equations are same , the system has infinite solutions

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The correct answer is option C. The system has a nontrivial solution.

One way to determine if a system has a nontrivial solution is to use Gaussian elimination to reduce the augmented matrix to row echelon form. If the row echelon form has a row of zeros except for the last entry in the augmented part, then the system has only a trivial solution.

If there is a row of zeros in the row echelon form that corresponds to a free variable, then the system has a nontrivial solution. In this case, it is possible to use Gaussian elimination to see that the row echelon form of the augmented matrix has a row of zeros except for the last entry in the augmented part, which is not zero, indicating that the system has a nontrivial solution.

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Answer:

[tex]x_1 + x_2 = \boxed{-5}[/tex]

Step-by-step explanation:

[tex]\mathrm{For\:a\:quadratic\:equation\:of\:the\:form\:}ax^2+bx+c=0\mathrm{\:the\:solutions\:are\:}[/tex]

[tex]x_{1,\:2}=\dfrac{-b\pm \sqrt{b^2-4ac}}{2a}[/tex]

[tex]\implies x_{1,\:2}=\dfrac{-b}{2a}\pm\dfrac{\sqrt{b^{2}-4ac}}{2a}[/tex]

Let's have

[tex]x_{1}=\dfrac{-b}{2a}+\dfrac{\sqrt{b^{2}-4ac}}{2a}[/tex]\

[tex]x_{2}=\dfrac{-b}{2a}-\dfrac{\sqrt{b^{2}-4ac}}{2a}[/tex]

[tex]x_1 + x_2 =\dfrac{-b}{2a}+\dfrac{\sqrt{b^{2}-4ac}}{2a} + \dfrac{-b}{2a}-\dfrac{\sqrt{b^{2}-4ac}}{2a}\\[/tex]

[tex]\dfrac{\sqrt{b^{2}-4ac}}{2a} - \dfrac{\sqrt{b^{2}-4ac}}{2a} = 0\\\\[/tex]

Leaving us with
[tex]\dfrac{-b}{2a} + \dfrac{-b}{2a}\\\\\implies 2 \cdot \left(\dfrac{-b}{2a}\right)\\\\\implies -\dfrac{b}{a}\\\\[/tex]

The given equation is
[tex]3x^2+15x+9=0[/tex]

Here a = 3, b = 15

So
[tex]-\dfrac{b}{a} = --\dfrac{15}{3} = -5\\[/tex]

Answer:
[tex]x_1 + x_2 = \boxed{-5}[/tex]

Answer:

17

Step-by-step explanation:

The original price was $20, so the discount price would be 20 * 15% = $3.

Therefore, the sale price would be 20 - 3 = $17.

When the expression y² + 10 y + 33 is written as a combination of a square of a binomial expression and an integer, the value of the integer is 8

We are given an expression y² + 10 y + 33 and this expression can be written as a combination of a square of a binomial and an integer. we need to find the value of the integer.

                        = y² + 10 y + 33

Write 10 y = 2 (5) (y)

                        = y² + 2 (5) (y) + 33

Write 33 = 25 + 8

                        = y² + 2 (5) (y) + 25 + 8

Write 25 = 5²

                        = y² + 2 (5) (y) + 5² + 8

Write y² + 2 (5) (y) + 5² = (y + 5)²

                        = (y + 5)² + 8

So, here (y + 5)² is the square of the Binomial expression and 8 is the integer.

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The probability that the ball will fall into a red slot during the following spin is 0.14.

To calculate the probability of an occurrence, divide the total number of outcomes by the total number of possible outcomes. The concepts of probability and odds are distinct. Odds are determined by dividing the probability of a situation happening by the probability that it won't happen. Probability is a metric used to determine how likely an event is to occur. When we toss the coin in the air, the probability that it will land with the heads side up is calculated. Here is a practical use of probability that you are probably already familiar with. We always check the weather forecast before a significant outing.

[tex]\frac{1}{7}=0.142857[/tex]

The probability is 0.14

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The probability of the ball landing on a red slot in a single spin of a fair roulette wheel is 1/2, as there are an equal number of red and black slots.

The outcome of each spin is independent, meaning that the outcome of one spin does not affect the outcome of another. Therefore, the probability that the ball will land on a red slot in the next spin is still 1/2, regardless of the results of the previous seven spins.

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