How do you find the relationship between zeros and the coefficients of a cubic polynomial?.

When x and y are directly proportional and when x is halved then y is also halved or (C) it is multiplied by 1/2.

DIRECTLY PROPORTIONAL: connected, i.e., one grows or shrinks in proportion to the other. His income is directly correlated with the number of units he sells.

If we spend Rs. 50 on two pens, as an example.

For four pens, it will cost us 100 Rs.

When the ratio x:y1 is constant, two values, x and y, are said to be inversely proportional to one another.

So, if a relationship between two variables, x and y, can be represented in the form y/x = k OR y = kx, it represents a proportionate variation.

Then,

If x rises, y will follow.

If x declines, y will follow.

So, we obtain:
When x is cut in half, y does as well.

Therefore, when x and y are directly proportional and when x is halved then y is also halved or (C) it is multiplied by 1/2.

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Correct question:
Two quantities, x and y, are directly proportional. If x is halved, what happens to y?

a. clear check it is doubled.

b. It is squared.

c. It is multiplied by 1/2.

d. It depends on the starting value of x.

By solving the equation we know that 15 players can be brought to the tournament.

Algebraically speaking, an equation is a statement that shows the equality of two mathematical expressions.

For instance, the two equations 3x + 5 and 14, which are separated by the 'equal' sign, make up the equation 3x + 5 = 14.

So, we know that:

Softball players raised $1186.50 to attend a tournament.

They allocated $21.50 for meals per player and paid $842.50 for the bus rental.

We must apply the following calculation to determine the total number of players they are permitted to bring:

Formula: Total amount of money= fixed cost + unitary variable cost × number of players

1186.50 = 842.50 + 21.50 × number of players

1186.50 - 842.50 = 21.50 × number of players

344/21.50 = number of players

15 = Number of players

Therefore, by solving the equation we know that 15 players can be brought to the tournament.

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The required relative frequency based on the frequency distribution of the students is 8.33%

The relative frequency is the frequency fraction of the number of observations the events occur to the total number of observations. The relative frequency provides a clear understanding of the distribution. This also helped to make a histogram and chart.

The number of times a value appears in a dataset is its frequency. The pattern of frequencies for a variable is known as a frequency distribution. The frequency with which each potential value of a variable appears in a dataset.

The frequency distribution is given.

Total number of student=36

The relative frequency for the class with lower-class limit 31 is calculated as;

R.F=No. of students in class interval/Total no.of students

=3/36

=0.0833

=8.33%

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Answer: The zero of a function is the value of y when x equals zero.

Step-by-step explanation:

The zero of a function is the value of y when x equals zero. It is also known as an x-intercept. In this case, the zero lies at (0,3) where x is zero and y is positive 3.

Answer:

a. 4 b.8

Step-by-step explanation:

a.

0 ∈ x<5

f(x)=x+4

f(0)=0+4=4

b.

6 ∈ 5≤x<7

f(x)=8

f(6)=8

By using the concept of Testing of Hypothesis, it can be concluded that

There has been no significant decrease in mean time per mile

What is Testing of Hypothesis?

Testing of Hypothesis is a method of inferencing which is used to decide whether a particular hypothesis can be supported with the help of the data at hand.

Completion time                  Completion time                     Difference

before training                     after training                                            

  5.9                                            5.4                                            0.5

  7.5                                            7.1                                             0.4                  

  6.1                                            6.2                                           -0.1

  6.8                                           6.5                                             0.3

   8.1                                            7.8                                            0.3

Mean for the completion before training = [tex]\frac{5.9 + 7.5 + 6.1 + 6.8 + 8.1}{5} = 6.88\\[/tex]

Mean for the completion after training = [tex]\frac{5.4 + 7.1 + 6.2 + 6.5 + 7.8}{5} = 6.6\\[/tex]

Mean for the difference = [tex]\frac{0.5 + 0.4 -0.1 + 0.3 + 0.3}{5} = 0.28\\[/tex]

Standard deviation for the completion before training = [tex]\sqrt{\frac{(5.9-6.88)^2 + (7.5-6.88)^2 + (6.1-6.88)^2 + (6.8-6.88)^2 + (8.1-6.88)^2}{5} }= 0.928\\[/tex]

Standard deviation for the completion after training = [tex]\sqrt{\frac{(5.4-6.6)^2 + (7.1-6.6)^2 + (6.2-6.6)^2 + (6.5-6.6)^2 + (7.8-6.6)^2}{5} }= 0.908\\[/tex]

Standard deviation for the completion after training = [tex]\sqrt{\frac{(0.5-0.28)^2 + (0.4-0.28)^2 + (-0.1-0.28)^2 + (0.3-0.28)^2 + (0.3 - 0.28)^2}{5} }= 0.228\\[/tex]

The null hypothesis [tex]H_0 : \mu_d = 0[/tex]

The alternate hypothesis [tex]H_a = \mu_d < 0[/tex]

Here left tail test is used

Critical value of t at [tex]\alpha = 0.05[/tex] and Degree of Freedom = 5 - 1 = 4

is [tex]t_c[/tex] = -2.132

t = [tex]\frac{0.28}{\frac{0.228}{\sqrt{5}}} = 2.746[/tex]

Since 2.746 > -2.132, the null hypothesis is accepted

So there has been no significant decrease in mean time per mile

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The greatest common multiple of 10 and 40 is 10.

The greatest common divisor (GCD) of two or more integers, where at least one of them is not zero, is the largest positive integer that is a divisor of both numbers. For example, the GCD of 8 and 12 equals 4.

In the divisibility preorder relation, the GCD of a and b is their greatest positive common divisor. This signifies that a and b's common divisors are the same as their GCD divisors. The Euclidean algorithm or Euclid's lemma are widely used to establish this. This is the definition of "greatest" in the context of GCD generalizations.

Foe calculating the GCD of 10 and 40, we have to find the factors of 10 and 40.

Factors of 10:

1, 2, 5, 10

Factors of 40:

1, 2, 4, 5, 10, 20, 40

From all these factors we have to choose the greatest factor that is exactly divisible by both 10 and 40 are 1, 2, 10, and 5.

So, the greatest common multiple of 10 and 40 is 10.

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The total ways are there for her to select the schedule for the week =  [tex]\frac{22!}{15!}} \\\\[/tex]  

Given, She makes 22 different dishes for each of the seven days of the week.

Total ways are there for her to select the schedule for the week = [tex]$ ^{22}P_7[/tex]

As We know,

[tex]$ ^nP_k=\frac{n!}{(n-k)!}} \\[/tex]

[tex]$ ^{22}P_7=\frac{22!}{(22-7)!}} \\\\[/tex]

[tex]\ $ ^{22}P_7=\frac{22!}{15!}} \\\\[/tex]

Hence, The total ways are there for her to select the schedule for the week =  [tex]\frac{22!}{15!}} \\\\[/tex]  

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Volume(V) of a sphere = 4πr^3

Charge within a small volume 'dV' is given by:

dq = ρ(r)dV

ρ(r) = C/r^2

Volume(V) of a sphere = 4/3(πr^3)

dV/dr = (4/3)×3πr^2

dV = 4πr^2dr

Therefore,

dq = ρ(r)dV ; dq =ρ(r)4πr^2dr

dq = C/r^2[4πr^2dr]

dq = 4Cπdr

FOR TOTAL ENERGY CHANGE 'Q', we integrate dq

∫dq = ∫4Cπdr at r = R and r = 0

∫4Cπdr = 4Cπr

Q = 4Cπ(R - 0)

Q = 4CπR - 0

Q = 4CπR

C = Q/4πR

Therefore, in the total energy change with all the terms given, the value of constant C in terms of Q, π and R is [Q/4πR].

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The given variation y = 7x is a direct variation where any increase in the variable x also increases the value of the variable y.

The given variation is represented as -

y = 7x

We have to identify if the given variation is direct or inverse or joint or combined.

Let us first the different mathematical relationships mentioned here.

Now that we know the definitions of different types of variations, let us look into the given variation, which is -

y = 7x

We can see that the variable y is 7 times the multiple of another variable x. Thus, this is a case of direct variation such that any increase in the variable x also increases the value of the variable y.

Therefore, the given variation y = 7x is a direct variation type.

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The coordinates of the turning point on the curve with the equation y = 9 + 18x - 3x² is (3,36).

Any equation of the form [tex]axx^{2} + bx + c = 0[/tex] where x is variable and a, b, and c are any real numbers where a ≠ 0 is called a quadratic equation.

It is given that:

The quadratic equation is:

y = 9 + 18x - 3x²

To find the turning point:

Graph the above quadratic equation;

From the graph:

The maximum point from where the graph starts to decrease is (3,36)

Thus, the coordinates of the turning point on the curve with the equation y = 9 + 18x - 3x² is (3,36).

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The value of r is found as 3/2 such that line that passes through the pair of points.

The slope is given bye the equation;

m = (y2 - y1)/(x2 - x1)

For the given question, the points are given as;

(x1, y1) = (r, -5),

(x2, y2) = (3, 13)

m = 8

8 = (13 + 5)/(3 - r)

8(3 - r) = 18

8r = 6

r = 3/2

Thus, the value of r is found as 3/2 such that line that passes through the pair of points.

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The correct question is-

Find the value of r so the line that passes through each pair of points has the given slope. (r, -5), (3, 13), m = 8

A formula for the nth term of the sequence is [tex]a_n[/tex] = 2n+1.

Given:

A sequence follows a plus 2 pattern: 3, 5, 7, 9, ...

here

first term a = 3

common difference d = 5-3

= 2

here common difference is same throughout the sequence so given sequence are in Arithmetic progression.

so nth term:

[tex]a_n = a+(n-1)d[/tex]

= 3 + (n-1)2

= 3+2n-2

= 2n+1

Therefore  A formula for the nth term of the sequence is [tex]a_n[/tex] = 2n+1.

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Here is the answer

1. Landing in a shaded portion and landing on 3

2. landing on a unshaded portion and landing on a  number less than 2

Events that do not occur simultaneously are said to be mutually exclusive. When a coin is tossed, for instance, the outcome will either be head or tail, but we cannot get both outcomes.

Events with no intersection are called mutually exclusive event.

What is being asked of us now.

Landing on a shaded portion means landing on either 1 or 4, as landing on 3 is impossible and will only result in landing on 3. So, there is no overlap between these occurrences.

Landing on an unshaded portion means landing on either 2 or 3.  And landing on a number less than 2 means landing on 1.

There is no intersection.

So these events are mutually exclusive.

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For the given binomial expression the coefficients of (a+b)³ are 1, 3, 3, 1

The constant coefficient is the coefficient that is not connected to any variables in an expression. For example, the constant coefficients in the formulas above are 3 and c, respectively. The leading coefficient is the coefficient associated to the variable with the highest degree in a polynomial. For example, in the formulas above, the leading coefficients are 2 and a, respectively.

We have,

The binomial expansion (a + b)³,

We know that,

The formula for binomial expansion,

(u + v)ⁿ = ⁿC₀uⁿv⁰ + ⁿC₁uⁿ⁻¹v¹ + ⁿC₂uⁿ⁻²v² + ⁿC₃uⁿ⁻³v³

Now,

u = a,

v = b,

And, n =3

Now,

By putting values,

(a + b)³ = ³C₀a³b⁰ + ³C₁a³⁻¹b¹ + ³C₂a³⁻²b² + ³C₃a³⁻³b³

(a + b)³ = ³C₀a³b⁰ + ³C₁a²b¹ + ³C₂a¹b² + ³C₃a⁰b³

Now,

By using combination formula,

On solving we get,

(a + b)³ = a³+3a²b+3ab²+b³

So,

Now,

The coefficients of :

a³ = 1,

3a²b = 3,

3ab² = 3,

b³ = 1,

So,

For the given binomial expression the coefficients of (a+b)³ are 1, 3, 3, 1

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Answer: the answer is d

Step-by-step explanation:

I took the tes

He has enough memory space to download a song that will use 0.12 gigabytes of memory

The memory capacity of new cell phone = 1.5 gigabytes

The memory capacity that already used = 1.35 gigabytes

The remaining space = The memory capacity of new cell phone  - The memory capacity that already used

Substitute the values in the equation

Here we have to use the subtraction

The remaining space = 1.5 - 1.35

Subtract the terms

= 0.15 gigabytes

The size of the song = 0.12 gigabytes

We know 0.15 > 0.12

Hence, he has enough memory space to download a song that will use 0.12 gigabytes  of memory

The complete question is

Devin has a new cell phone that holds 1.5 gigabytes if memory for music. He has already used 1.35 gigabytes of the memory. Will he have enough space to download a song that will use 0.12 gigabyte of memory? Explain.

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The equation 4x + 2(x -5) = 3(2x - 4) does not have any solutions.

From the given equation:

We have 4x + 2(x -5) = 3(2x - 4)

By opening the brackets, we have:

2x+ 4x + - 10 = 6x - 12

6x - 10 = 6x - 12

By collecting the like terms, we have:

6x - 6x = -12 + 10

0 = -2

Thus, since there is no constant to a variable, then there is absolutely no solution at all.

An equation is deemed to be linear if the greatest power of the variable is consistently 1. It is also referred to as the one-degree equation. A linear equation with one variable typically has the form Ax + B = 0.

In this case, the variables x and A are the variables while only the variable B is a constant. A linear equation with two variables often has the form

Ax + By = C. The variables x and y, the coefficients A and B, and the constant C are present in this scenario.

Disclaimer : the complete question is :

How many solutions does the equation 4x + 2(x -5) = 3(2x - 4) have?.

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Answer:  4 pencil

Step-by-step explanation:

The width of the rectangular walkway is 3 feet around.

The walkway has a uniform width around the rectangle.

Let the width of walkway be x

The total length of the garden and walkway will be (12+2x) feet

The total width of the walkway and garden would be (8+2x) feet

Area of the garden and the walkway together are 252 square

Let’s express this mathematically:

(8+2x)(12+2x) = 252

Let’s open the brackets;

96+ 16x+ 24x + 4x^2 = 252

4x^2 + 40x + 96 = 252

4x^2 + 40x + 96-252 = 0

4x^2 + 40x - 156 = 0

Let’s divide all through by 10. We have;

x^2 + 10x -39 = 0

X^2 +13x-3x-39 = 0

x(x + 13) -3(x+ 13) = 0

(x-3)(x + 13) = 0

x -3 = 0 or x + 13 = 0

x = 3 or -13

We ignore x = -13 since width cannot be negative in size

Therefore, the width of the rectangular walkway is 3 feet around.

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The probability that this person is a graduate student is 0.3833.

From the recent census

40% of its students mainly used Ma- cintosh computers.

At the time of the census, 67% of the school's students were undergraduates.

In the census, 23% of the respondents were graduate students who said that they used PCs as their primary computers.

We have to find the probability that this person is graduate student.

Let A represent the event that student uses Mac.

So P(A)=40%=0.4, P(A')=60%=0.6

Then let B be the event that randomly chosen student is undergraduate·

So, P(B) = 67%=0.67, P(B')= 33%=0.33

Further, 23% of respondents were graduate. Students who said they used PCs as their Primary Computers

So P(B'∩A')=23%=0.23

If we select a student at random from among those who were part of the Census and learn that student mainly uses PC, then probability that this person is a graduate student is:

P(B'|A') = P(B'∩A')/P(A')

P(B'|A') = 0.23/0.6

P(B'|A') = 0.3833

Hence, the probability that this person is a graduate student is 0.3833.

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The right question is:

Mac or PC? A recent census at a major university revealed that 40% of its students mainly used Ma- cintosh computers (Macs). The rest mainly used PCs. At the time of the census, 67% of the school's students were undergraduates. The rest were gradu- ate students. In the census, 23% of the respondents were graduate students who said that they used PCs as their primary computers. Suppose we select a student at random from among those who were part of the census and learn that the student mainly uses a PC. Find the probability that this person is graduate student. Show your work.

Answer:

4.2

Step-by-step explanation:

you look at where x=-1.5 and it’s about 4.2 where it is

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The probability that she succeeds at fewer than 7 free-throws is 0.19

The table of values is given as

5: 0 successes

6: 5 successes

7: 8 successes

8: 6 successes

9: 6 successes

10: 1 success

From the above readings, the throws less than 7 are

5: 0 successes

6: 5 successes

So, the number of success is

Success = 0 + 5

Success = 5

The probability is then calculated as

P = Success/Total

So, we have

P = 5/(0 + 5 + 8 + 6 + 6 + 1)

Evaluate

P = 5/26

So, we have

P = 0.19

Hence, the probability is 0.19

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The total cost of the ticket is AED 160.

What is the ticket price?

The term "ticket price" refers to the whole cost of a ticket, which includes the airfare as well as all applicable taxes, fees, surcharges, and charges for all optional and required services.

Given,  6 adults pay AED 20 each

And, 4 children pay AED 10 each

So, total cost of the ticket = 6*20 + 4*10 = 120 + 40 = 160

Hence, the total cost of the tickets is AED 160.

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The required  local maximum and minimum values of f using both the First and Second Derivative Tests.

The local maxima is a point inside a stretch at which the capability has a most extreme worth. The outright maxima is likewise called the worldwide maxima and is the point across the whole area of the given capability, which gives the most extreme worth of the capability.

The local minima is the info an incentive for which the capability gives the base result values. The capability condition or the diagram of the capability isn't once in a while adequate to see as the nearby least. The subordinate of the capability is exceptionally useful in tracking down the nearby least of the capability.

f(x)=x/x^2+9

differentiate with respect to x

df(x)/dx = d(x/x^2+9)/dx = -2/x^2+2x^2/9

second derivative = 3/x^3+2x^3/3

Put this derivative equal to zero, then we will put given points, if it becomes negative then the point is on maxima, if it is positive then is on minima.

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There were 1575 boys and 945 girls.

A ratio is an ordered pair of numbers a and b, written a / b where b does not equal 0. A proportion is an equation in which two ratios are set equal to each other. For example, if there is 1 boy and 3 girls you could write the ratio as 1 : 3.

A ratio is a number with no units.

According to the information provided to us, there were 3 girls for every 5 boys.

3 to 5 girls to boys are the ratio.

The sum is 8.

We need to find the number of girls and boys

Out of 2,520, 3 to 5 girls were present.

We have 3/8(2520) = 7560/8 girls, which comes to 945.

For boys, 5/8(2520) = 12600/8 boys, which equals 1575.

Therefore, there were 945 girls and 1575 boys respectively.

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two polynomials are relatively prime if the greatest common divisor of the two polynomial is 1

How do you prove two polynomials are relatively prime?

Two polynomials from Z[x] are called evaluationally relatively prime if the greatest common divisor of the two polynomials in Z[x] is 1 and gcd(f(t),g(t)) = 1 for all t ∈ Z.

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In this problem, 0.22 is a parameter.

Mean is defined as the average of given numbers i.e. sum of all numbers divided by the total number of numbers. The Mean is denoted as m or μ. Standard deviation is the measure which it shows the variation from the mean exists or not. The standard deviation is denoted as σ.

The range of possible values for a variable is known as a parameter. A parametric equation is an equation expressed in terms of parameters. In the equation y = 2x + 1, x is called the parameter. In statistics, a function variable whose variable is sought by means of evidence from the samples is called a parameter.

As per the given question,

⇒ 0.22 is the standard deviation of the random sample which is a measurement. Measurements of populations can be called parameters.

Therefore, the 0.22 value in the problem is called a parameter.

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The complete question is

A random sample of 121 bottles of cologne showed an average content of 4 ounces. it is known that the standard deviation of the contents (i.e., of the population) is 0.22 ounces. In this problem, the value 0.22 is

A. a parameter

B. a statistic

C. the margin of error for a confidence interval

D. the average content of colognes in the long run

E. none of the above

The expression that shows how many hot dog buns were ordered is 8p.

Expression simply refers to the mathematical statements which have at least two terms which are related by an operator and contain either numbers, variables, or both.

Given that the school cook ordered p packages of hot dog buns for the year-end picnic and each package contains 8 buns.

The expression will be the multiplication of the variables. This will be:

= 8 × p

= 8p

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The empirical rule states that, for data having a bell-shaped distribution, the portion of data values being within one standard deviation of the mean is 68%

A bell curve is the informal name of a graph that depicts a normal probability distribution. The term obtained its name due to the bell-shaped curve of the normal probability distribution graph.

The bell curve is perfectly symmetrical. It is concentrated around the peak and decreases on either side.

The dispersion of the data on the bell curve is measured by the standard deviation.

According to the question,

The empirical rule states that, for data having a bell-shaped distribution, the portion of data values being within one standard deviation of the mean is 68%

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