Is the leading coefficient of the polynomial function negative or positive?.

As per the given total number of chocolates, and the number of chocolates given to his friends and the left chocolates , the number of friends at Jack's party were equal to 16.

As given in the question,

Total number of chocolates given by Jack's mother is equal to 50

Number of chocolates given by Jack to his friends = 3

Number of chocolates left with Jack = 2

Let 'x' represents the number of friends

Requires equation to show the relation we have,

3x + 2 = 50

⇒ 3x = 50 - 2

⇒ 3x = 48

⇒ x = 48/ 3

⇒ x= 16 friends

Therefore, for the given total number of chocolates, and the number of chocolates given to his friends and the left chocolates , the number of friends at Jack's party were equal to 16.

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The following inequalities are equivalent to the inequality 5 < -y + b.

y< b - 5 and b - 5 > y

What is inequality?

An inequality in mathematics depicts the connection between two values in an algebraic statement that are not equal. One of the two variables on the two sides of the inequality may be greater than, greater than or equal to, less than, or less than or equal to another value, according to inequality signals.

5 < -y + b

Adding or subtracting the same quantity from both sides of an inequality leaves the inequality symbol unchanged

5 < -y + b

Add y on both the sides, we get

5+y < b

subtract 5 on both sides

y< b - 5

 Interchange the expressions .So inequality symbol changes

b - 5 > y

So, the following inequalities are equivalent to the inequality 5 < -y + b.

y< b - 5 and b - 5 > y

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Answer:

question 1 isn't formatted properly, for question 2, k=-2

Step-by-step explanation:

5k-8+2=-16

5k-6=-16

5k=-10

k=-2

To calculate the interest and the total amount , we use Simple interest formula S.I = ( P× r × t ) / 100.

Simple interest is a method of calculating the interest that is charged on fixed deposits , savings accounts and the loans .

The money you put in the bank is called the principal, the bank pays you interest.

The interest is computed as a certain percent of the principal; called the rate of interest. The rate of interest is usually expressed as a percent per year, and is calculated by using the decimal equivalent of the percent.

The variable for time, t, represents the number of years the money is left in the account.

The formula to calculate simple interest is :

S.I = ( P× r × t ) / 100

where P is principle , r = rate of interest and t is term of loan in year.

To use the simple interest formula we substitute in the values for variables that are given, and then solve for the unknown variable.

To find the total amount ,

Amount = Principle + Interest

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Answer:

Step-by-step explanation:

again , you know that the two angles add up to 180°

you know that by the complementary angle rule.

set the two equations equal to 180 and solve for x

180= eq1 + eq2

The maximum speed is 3667 m/s if the engine can impart a force of 4522 N on the road.

What is Drag coefficient?

The aerodynamic drag coefficient is a measure of the effectiveness of a streamline aerodynamic body shape in reducing the air resistance to the forward motion of a vehicle.

Given that,

mass of a car(ρ) = 1834 kg

drag coefficient (c) = 0.342 kg/m

Force(F) = 4522 N

and we have to find maximum speed.

We know the formula for Drag coefficient,

c = 2F/ ρu^2

⇒ u^2 = 2F/ ρc

          = 2(4522)/1834×0.342

          = 9044 / 672.2

   u^2 = 13.454

       u = 3.667

       u = 3667 m/s

Therefore maximum speed is 3667 m/s.

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The statements K-means is extremely sensitive to cluster centroid initializations and Poor initialization can lead to slow convergence are true. Option A and option C are correct.

K-means Clustering is a vector quantization technique that seeks to split "n" observations into "k" clusters, with each observation referring to the cluster with the closest mean, which reflects a model of the cluster.

This means that the K-means algorithm recognizes the "k" number of centroids and then allocates every data point to the cluster with the fewest centroids.

Thus, the statements K-means is extremely sensitive to cluster centroid initializations and Poor initialization can lead to slow convergence are true. Option A and option C are correct.

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Answer:

A.2

Step-by-step explanation:

The required difference in the speed of Grayson ans Maya is 2 miles per hour.

Speed is characterized as. The pace of progress of position of an article toward any path. Speed is estimated as the proportion of distance to the time in which the distance was covered. Speed is a scalar amount as it has just bearing and no extent.

Grayson biked 45 miles in 3 hours

His speed = 45/3 = 15 miles/hour

Similarly,

Maya biked 26 miles in 2 hours

So, his speed = 26/2 = 13 miles /hour

Difference in their speed = 15-13 = 2 miles per hour

Thus, Speed of Grayson is 2 miles/hour greater than Maya.

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The number of layers of cubes present in the rectangular prism of volume 102/3 in³ is 7.

Volume is defined as the space occupied within the boundaries of any three-dimensional solid.

To calculate the number of layers of cubes in the prism, we use the formula below.

n = V/9l³............Equation 1

Where:

From the question,

Given:

Substitute these values into equation 1

Hence, there are 7 layers in the rectangular prism.

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Since the number of roots of a polynomial function is equal to the highest degree of the polynomial function, the total number of roots of the given polynomial functions are 6 and 2 respectively.

We have two polynomial functions given by -

[tex]F(x) = 3x^{6}+2x^{5}+x^{4}-2x^{3}[/tex] ----- (1)

[tex]G(x)=5x-12x^{2} +3[/tex] ---- (2)

We have to find out the total number of roots of each polynomial function.

We know that, the number of roots of a polynomial function is equal to the highest degree of the polynomial function.

In equation (1), we have

[tex]F(x) = 3x^{6}+2x^{5}+x^{4}-2x^{3}[/tex]

Here, we can see that the highest degree of the polynomial function F(x) is 6 which is the highest degree of x in the polynomial.

So, the total number of roots of the polynomial function F(x) is 6.

Similarly, in equation (2), we have

[tex]G(x)=5x-12x^{2} +3[/tex]

Here, we can see that the highest degree of the polynomial function G(x) is 2 which is the highest degree of x in the polynomial.

So, the total number of roots of the polynomial function G(x) is 2.

Therefore, the total number of roots of the given polynomial functions are 6 and 2 respectively.

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It takes 12 hours to drive to Atlanta. Using the distance-time-speed formula the required time is calculated.

What is the distance?

Distance is the sum of an object's movements, regardless of direction. The distance can be defined as the amount of space an object has covered, regardless of its starting or ending position.

Given that,

The distance to uncle's house = 728 miles

The time taken to drive to uncle's house = 14 hours

So,

speed = (728)/14 = 52 miles/hour

Then the time to drive 624 miles(to Atlanta) is calculated by,

time t = (624)/52 = 12 hours.

Hence,  It takes 12 hours to drive to Atlanta. Using the distance-time-speed formula the required time is calculated.

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Answer:

[tex]z\leq 16.1[/tex]

Step-by-step explanation:

-4z>=-64.4

/-4.    /-4

z>=16.1

And when we switch the signs we switch which was the alligator points

z<=16.1

Hopes this helps please mark brainliest

Answer:

z ≤ 16.1

Step-by-step explanation:

Given inequation,

→ -4z ≥ -64.4

Now the value of z will be,

→ -4z ≥ -64.4

→ z ≤ -64.4/-4

→ z ≤ 64.4/4

→ [ z ≤ 16.1 ]

Hence, the value of z is 16.1.

The scale factor of the dilation of triangle DEF is 3/10

Given,

Triangle DEF's scale factor of dilation is equal to the ratio of its corresponding sides to those of triangle D'E'F':

f = D'F'/DF = D'E'/DE = E'F'/EF scale factor (1)

The comparable triangles OD'F' and ODF can be used to calculate the ratio D'F'/DF because their sides must be proportional:

D'F'/DF = OF'/OF = OD'/OD (2) (2)

According to the figure, we understand:

If F'F = 7 and OF' = 3, then

OF = OF' + F'F → OF = 3 + 7 → OF = 10

Then substituting in (2):

(2) DF/DF = 3/10 = OD/OD

Also substituting in (1):

(1) f = 3/10 = E'F'/EF = D'E'/DE

That is,

The scale factor of the dilation of triangle DEF is 3/10

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The question is incomplete. Completed question is given below;

What is the scale factor of the dilation of triangle DEF?

Figure is attached;

Options A,B are true and the other 3 C,D,E are false.

What is matrix?

The arrangements of numbers, variables, symbols, or phrases in a rectangular table with varying numbers of rows and columns are known as matrices, which is the plural version of the word matrix. They are rectangular arrays with defined operations for addition, multiplication, and transposition. The constituents of the matrix are its numbers or entries. Vertical entries in matrices are referred to as columns, whereas horizontal entries are known as rows. A matrix is a rectangular array of numbers, variables, symbols, or expressions that are defined for operations like subtraction, addition, and multiplication. The number of rows and columns in a matrix determines its size, sometimes referred to as its order.

A) If Ax=λx for some vector x, then x is an eigenvector of A

if x not equal to 0 then the statement is true.

B) A steady-state vector for a stochastic matrix is actually an eigenvector:

As it is an egien vector the statement is true.

C) If v1 and v2 are linearly independent eigenvectors, then they correspond to distinct eigenvalues.:

the statement is false.

D) The eigenvalues of a matrix are on its main diagonal:

It's only true for the trigonal matrix.

E) An eigenspace of A is just a null space of a certain matrix:

the statement is false.

Hence we have determined the true and false statement from the given option.

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The function f(x) = (3/4)ˣ has its graph to be graph (a) and the table to be:

x  -2       -1      0     1      2

y  16/9   4/3   1     3/4   9/16

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

f(x) = (3/4)ˣ

This function is an exponential function

The x values present on the tables of values are

x = -2, -1, 0, 1 and 2

These values are to be used to calculate the f(x) values of the function

To do this, we simply substitute x = -2, -1, 0, 1 and 2 f(x) = (3/4)ˣ

The above highlights give:

f(-2) = (3/4)⁻² = 16/9

f(-1) = (3/4)⁻¹ = 4/3

f(0) = (3/4)⁰ = 1

f(1) = (3/4)¹ = 3/4

f(2) = (3/4)² = 9/16

This means that the table of values is

x:  -2       -1      0     1      2

y:  16/9   4/3   1     3/4   9/16

Next, we plot the graph of the function using the values in the above table

The graph that passes through the points in the above table (i.e. (-2, 16/9), (-1, 4/3).....)  is graph (a)

Hence, the graph of the function is graph (a)

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The correct answer is 0.75x + 0.15y = 90 is the equation that describes the quantity of pens and pencils the glee club can purchase.

The maximum number of pens the club can purchase is 120.

The maximum number of pencils the club can purchase is 600.

Each pen costs $0.75.

Total number of pens = x

Each pencil costs $0.15

y = number of pencils

(Cost of each pen) x (Number of pens) + (Cost of each pencil) x (Number of pencils) = $90 which equals the total cost for pens and pencils.

The formula for the quantity of club pens and pencils is 0.75x + 0.15y = 90.

When 0.75x = 90

x = 90/0.75

x = 120, the club purchases the most pens.

The maximum number of pens the club can purchase is 120.

When the club purchases the most pens, 0.15x = 90

x = 90/0.15

x = 600

Hence, the maximum number of pencils the club can purchase is 600 and the formula for the quantity of club pens and pencils is 0.75x + 0.15y = 90.

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The values for the highlighted variables is a=-1,b=-9,c=9,d=3,e=3,f=2 and g=3/2.

Given:

3x/2x-6 + 9/6-2x

Rewrite 6-2x as 2x-6 by taking (-1) as common factor:

= 3x/2x-6 + 9/(-1)(2x-6)

so a = -1

= 3x/2x+6 + -9/2x-6

so b = -9

The LCM of 2x - 6 and 2x - 6 is 2x -6.

= 1*3x + 1*-9 / 2x-6

= 3x - 9 / 2x -6

so c = 9

(3x - 9) = 3(x-3)

(2x - 6) = 2(x - 3)

= 3(x-3)/2(x-3)

so d =3,e=3 and f=2 , g = 3/2.

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Full question:

Enter the values for the highlighted variables to complete the steps to find the sum:

3x/2x-6 + 9/6-2x = 3x/2x-6 + 9/a(2x-6) = 3x(2x-6)+6(2x-6)=3x-c 2x-6 =d(x-x) f(x-3) = g

A- -1

B= -9

C= 9

D= 3

E= 3

F= 2

G= 1.5

The  Bayes's theorem help us to take an better prediction of even with the help of another occuring event.

Bayes' theorem, in probability hypothesis, a method for reexamining expectations considering important proof, otherwise called restrictive likelihood or opposite likelihood. The hypothesis was found among the papers of the English Presbyterian clergyman and mathematician Thomas Bayes and distributed after death in 1763.

Bayes' theorem expresses that the contingent likelihood of an occasion, in view of the event of another occasion, is equivalent to the probability of the subsequent occasion given the principal occasion duplicated by the likelihood of the main occasion.

This theorem gives us an idea to take better prediction of the event.

Option(a)  to help you make a better decision is correct answer.

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Dyan must show harm to recover damages as he claims to have access to a stock-trading algorithm that will multiply an investment many times over.

What is algorithm?

In arithmetic and computing, an algorithm could be a finite sequence of rigorous directions, generally wont to solve a category of specific issues or to perform a computation. Algorithms ar used as specifications for acting calculations and processing.

Main body:

As he has the access to to a stock-trading algorithm , it becomes his obliged duty to help the customer with his recovery damages.

Hence , Dyan must show harm to recover damages

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Any number that represents something other than zero is considered to be positive.

In the given question we have to explain a positive number in math.

Any number that represents something other than zero is considered to be positive. When referring to the amount of money in your bank account, a positive figure would undoubtedly make you feel good as well.

The natural, or counting, numbers 1, 2, 3, 4 and 5 are examples of positive numbers, as are fractions like 8/5 or 32/45 and decimals like 49.4.

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The distance between the points (22,11) and (6,11) in the coordinate plane is 16 units.

According to the question,

We have the following information:

The two points in the coordinate plane = (22,11) and (6,11)

Now, we know that the following formula is used to find the distance between two points in the coordinate plane:

Distance between two points = [tex]\sqrt{(y2-y1)^{2} +(x2-x1)^{2} }[/tex]

We have the following values:

x1 = 22 and y1 = 11

x2 = 6 and y2 = 11

Distance between two points = [tex]\sqrt{(11-11)^{2} +(6-22)^{2} }[/tex]

Distance between two points = [tex]\sqrt{(-16)^{2} }[/tex]

Distance between two points = 16 units

Hence, the distance between the points (22,11) and (6,11) in the coordinate plane is 16 units.

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The quotient of division 2/( √13+√11) is (√13-√11).

A quotient is a quantity that is obtained by dividing two integers. The answer is D.

What is a quotient?

A quotient is a quantity that is obtained by dividing two integers. The quotient is a term that is widely used in mathematics to refer to the integer component of a division, as well as a fraction or a ratio.

In order to find the quotient of the fraction, we need to take the rationalize of the fraction.

= 2/(√13 + √11)

= 2/(√13 + √11) x (√13 - √11)/(√13 - √11)

= 2(√13 + √11)/(√13)^2 - (√11)^2

= 2(√13 - √11)/13-11

= 2(√13-√11)/2

= (√13-√11)

Hence the answer is, the quotient of division 2/( √13+√11) is (√13-√11).

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The slope of the line is m = - 3

What is the line's slope, please?

the equation of a line of slope-intercept form is given by

  y = mx + c

an equation of the form y = -3x + 2

now compare with equation

 m = -3

  c = 2

Thus, the slope of the line is m = - 3

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The complete question is -

What is the slope of the line y = -3x+2

The solution for the agebraic equation 20 = 5(7 -x) is x = 3, which is correct option from the solution set.

Algebra is the branch of mathematics that helps to represent problems or values in the form of mathematical equation or expression

Solving for the solution in the given algebraic equation;

20 = 5(7 -x)

20 = 35 - 5x (expand bracket)

also

5x + 20 = 35 - 5x + 5x {add 5x to both sides}

5x + 20 - 20= 35 - 20 + 20 {subtract 20 from both sides}

5x = 15

x= 15/5 {divide through by 5}

x = 3

Therefore, algebraic equation 20 = 5(7 - x) is true for the value of x = 3.

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The mean and standard deviation of a sampling distribution of sample means with sample size n=36 are 72,3

The act of deciding on the number of observations or replicates to include in a statistical sample is known as sample size determination. The sample size is an important aspect of any empirical study that seeks to draw conclusions about a population from a sample. In practice, the sample size employed in a study is frequently dictated by the cost, time, or convenience of gathering the data, as well as the necessity for statistical power. In complex research, sample sizes may vary: for example, in a stratified survey, sample sizes may fluctuate for each strata. Because data for an entire population is sought in a census, the targeted sample size is the population. During the experimental design process.

Given,

Mean μ=72

Standard deviation σ=18

Sample size n=36

The mean of the sample distribution is defined as:

E([tex]\bar{x}[/tex])=μ

E([tex]\bar{x}[/tex])=72

Standard deviation of a sample mean is,

SE([tex]\bar{x}[/tex])=σ/√n

SE([tex]\bar{x}[/tex])=18/√36

SE([tex]\bar{x}[/tex])=3

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The number of applications Jen can expect from the self-tanner is 22.5.

What is applications?
Mathematical Applications focuses on developing students' mathematical expertise in both established and novel contexts. Financial modelling, matrix, network analysis, route as well as project planning, decision-making, as well as discrete growth and decay are a few of these contexts.

What is an advertising claim?

An advertising claim is a statement made in advertising about the advantages, features, and performance of a good or service with the intention of convincing the consumer to buy it.

First, to determine how many applications 1 -oz of the bottle can provide.

Number of applications 1 -oz of the bottle can provide = 3/2 = 1.5

Second, to determine the number of applications 15 oz of the bottle can provide = 15 x 1.5 = 22.5 applications

Hence, the total number of applications expected is 22.5

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The four step to graphing the linear inequalities are: Always begin by separating the variable y from the inequality's left side, Replace the inequality symbol with the equality symbol, In XY plane, graph the boundary line from step 2, The final step is to shade a portion or one side of the border line.

In the given question we have to explain the 4 steps in graphing linear inequalities.

Step 1: Always begin by separating the variable y from the inequality's left side.

Step 2: Replace the inequality symbol with the equality symbol.

Step 3: In XY plane, graph the boundary line from step 2.

Step 4: The final step is to shade a portion or one side of the border line.

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The value of 5.37/3 is 1.79.

Calculate the answer using a math operator is referred to as a mathematical operation.

Basic mathematical operations are addition, multiplication, subtraction and division.

The given term is 5.37 divided by 3,

The mathematical expression for 5.37 divided by 3,

= 5.37/3

= 1.79

The value of 5.37 divided by 3 is 1.79.

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72 miles, distance travelled by Nakeisha's family when Nakeisha fell asleep.

Percentage is a part of the whole number. It is denoted by % sign.

1 %= 1/100.

Given that,

Total distance of the trip = 400 miles,

The percentage of distance when Nakeisha fell asleep = 18%.

The distance when Nakeisha fell asleep,

= 400×18/100

= 72 miles

The distance travelled by Nakeisha's family when Nakeisha fell asleep is 72 miles.

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