Solve the following:
a)
4x3 2x + 7
Optional working+
b)
2x + 6 = 7x-
-
Optional wor

The polynomial function is f(x) = x² - 49 if the leading coefficient is 1 or f(x) = -x² - 49 if the leading coefficient is -1.

Polynomials are expressions of the form,

a₀ + a₁ x + a₂ x² + ................. + aₙ₋₁ xⁿ⁻1 + aₙ xⁿ

where a's are the coefficients, x is the variable and n is the number of terms.

Given that, the degree of the function is 2.

So the function is quadratic.

It is of the form f(x) = ax² + bx + c.

The y - intercept is (0,-49).

Substituting the point,

(a × 0²) + (b × 0) + c = -49

c = -49

Function is f(x) = ax² + bx - 49.

We have, the x - intercepts are ( -7,0), (7,0).

Substituting the points, we get two equations.

a (-7)² + b (-7) - 49 = 0 and a (7)² + b (7) - 49 = 0

49a - 7b - 49 = 0 and 49a + 7b - 49 = 0

Subtracting 49a - 7b - 49 = 0 from 49a + 7b - 49 = 0, we get,

14b = 0

b = 0

So the function is of the form f(x) = ax² - 49.

Given that,  Assume the leading coefficient is 1 or -1.

Function is either f(x) = x² - 49 or f(x) = -x² - 49

Hence the required function is f(x) = x² - 49 or f(x) = -x² - 49.

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The given statement is true, The set of all possible outcomes during the course of an experiment is called a sample-space.

Sample-space, in probability, is referred to as the collection of all possible outcomes in any random experiment. It is denoted by "S".

Since it is a set, it is shown within the braces.

Given statement,

The set of all possible outcomes during the course of an experiment is called a sample-space.

By the definition of sample space, statement is true.

Example: Toss a coin

Sample-space, S={H,T}

H= head

T= tail

Hence, The set of all possible outcomes of any experiment is called sample-space.

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The electric field force does 1.90 x 10⁻⁸ J of work to move the two point charges from 0.30 m to 1.05 m apart.

The electric field is a vector field that represents the force experienced by a charged particle due to an electric charge distribution. It is a measure of the electric force per unit charge at a particular point in space. The electric field is defined as the negative gradient of the electric potential, which is the energy per unit charge that a charged particle would have at that point in space. The electric field can be used to calculate the force experienced by a charged particle in the presence of other charges, and is a fundamental concept in the study of electromagnetism.

The electric field force between two point charges is given by Coulomb's law:

F = k * (q₁ * q₂) / r²

where k is the Coulomb constant (8.99 x 10⁹ N m²/C²), q₁ and q₂ are the magnitudes of the charges, and r is the distance between the charges.

To calculate the work done by the electric field force, we need to find the force at the initial distance (0.30 m) and the final distance (1.05 m), and then subtract the work done at the initial distance from the work done at the final distance.

At a distance of 0.30 m, the force is:

F = k * (1.75 x 10⁻⁸ C)² / (0.30 m)² = 4.02 x 10⁻⁸ N

The work done at this distance is:

W = F * 0.30 m = 1.21 x 10⁻⁷ J

At a distance of 1.05 m, the force is:

F = k * (1.75 x 10⁻⁸ C)² / (1.05 m)² = 1.33 x 10⁻⁸ N

The work done at this distance is:

W = F * 1.05 m = 1.40 x 10⁻⁷ J

Finally, to find the total work done, we subtract the work done at the initial distance from the work done at the final distance:

W total = W final - W initial = 1.40 x 10⁻⁷ J - 1.21 x 10⁻⁷ J = 1.90 x 10⁻⁸ J.

Therefore, the electric field force does 1.90 x 10⁻⁸ J of work to move the two point charges from 0.30 m to 1.05 m apart.

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let's firstly convert the mixed fractions to improper fractions.

[tex]\stackrel{mixed}{7\frac{5}{6}}\implies \cfrac{7\cdot 6+5}{6}\implies \stackrel{improper}{\cfrac{47}{6}} ~\hfill \stackrel{mixed}{5\frac{1}{3}} \implies \cfrac{5\cdot 3+1}{3} \implies \stackrel{improper}{\cfrac{16}{3}} \\\\\\ \stackrel{mixed}{1\frac{1}{9}}\implies \cfrac{1\cdot 9+1}{9}\implies \stackrel{improper}{\cfrac{10}{9}} \\\\[-0.35em] ~\dotfill[/tex]

[tex]\left( \cfrac{47}{6}-\cfrac{16}{3} \right)+\cfrac{10}{9}\implies \cfrac{47}{6}-\cfrac{16}{3}+\cfrac{10}{9}\implies \cfrac{(3)47~~ - ~~(6)16~~ + ~~(2)10}{\underset{\textit{using this LCD}}{18}} \\\\\\ \cfrac{141-96+20}{18}\implies \cfrac{65}{18}\implies {\Large \begin{array}{llll} 3\frac{11}{18} \end{array}}[/tex]

Answer:

Deborah is 27 years old and Syria is 31 years old.

Step-by-step explanation:

Let's say Deborah's age is x and Syria's age is y.

From the given information, we know that:

x + y = 58 (the sum of their ages is 58)

Also, the difference between their ages is 4, which means:

y - x = 4

We can use these two equations to find the values of x and y.

First, we'll solve for y:

y = x + 4

Substituting this value of y into the first equation:

x + (x + 4) = 58

Expanding the left-hand side:

2x + 4 = 58

Subtracting 4 from both sides:

2x = 54

Dividing both sides by 2:

x = 27

So Deborah is 27 years old and Syria is y = 27 + 4 = 31 years old.

Answer:

1 wow

Step-by-step explanation:

The average confidence interval, according to our 80% level of confidence, falls between 31.54 and 35.86 minutes for the total population.

You only have a 5% probability of making a mistake with a 95% confidence interval. You have a 10% probability of being mistaken when the confidence interval is 90%. The difference between a 95 percent and 99 percent confidence interval is the width of the interval (for example, plus or minus 4.5 percent instead of 3.5 percent).

Confidence intervals include details about the range in which the true value is likely to fall, as well as the kind and magnitude of the effect that has been proved. Conclusions concerning the can be made as a result of this.

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Answer:

[tex](17 \times6) + (11 \times 4)[/tex]

[tex]102 + 44 = 146[/tex]

Standard deviation of data represents hours worked per day by entry level employees is 2.9

The following set of data represents hours worked per day by entry level employees :

14, 7, 10, 9

First calculate the mean of the sample

Mean ([tex]\overline{X}[/tex])= [tex]\frac{14+7+10+9}{4}[/tex]

Mean = [tex]\frac{40}{4}[/tex]

[tex]\overline{X}[/tex]  = 10

Now, calculate the standard deviation:

Standard deviation = [tex]\sqrt\frac{\sum{(x_i - \overline{X}})^{2}}{N -1}[/tex]

Standard deviation = [tex]\sqrt \frac{(14-10)^{2}+(7-10)^{2}+(10-10)^{2}+(9-10)^{2}}{3}[/tex]

Standard deviation = [tex]\sqrt\frac{16+9+0+1}{3}[/tex]

Standard deviation = [tex]\sqrt{8.66}[/tex] = 2.9

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Answer:

P(A∩B) = 0

P(A) = 0.1667

P(B) = 0.8333

=================================================

Explanation:

The events

are mutually exclusive. There isn't any overlap. This is because event B involves "at least 2 rolls", meaning we cannot get 5 on the first roll. Either event A happens, or B does, but not both at the same time.

This allows us to say P(A∩B) = 0

In a venn diagram, the overlapped region between circles A and B would have probability 0 marked inside.

-----------------------

P(A) = 1/6 since there is exactly one side labeled "5" out of 6 sides total. This converts to the approximate decimal form 1/6 = 0.1667 when rounding to four decimal places. The 6's go on forever, but of course we have to round at some point.

------------------------

We found that P(A) = 1/6. The complement to this is 1-(1/6) = 5/6, which is the probability of rolling anything but a "5". This fraction represents the scenario "at least 2 rolls are needed for the 1st '5' to show up" since we forced the first roll to be anything but 5.

Put another way, we have two options:

The two probabilities 1/6 and 5/6 add to 6/6, aka 1, to represent 100% of all possible cases. This means P(A)+P(B) = 1 for this scenario.

The fraction 5/6 converts to the approximate decimal form of 5/6 = 0.8333; use a calculator or long division to determine this value.

Answer:

1/12

Step-by-step explanation:

Total Number of pieces of paper = 24

Total Number of pieces of paper with an odd number on it= 24/2 = 12

Total Number of pieces of paper with Number 19 = 1

Probability of a student on blue team having the Number 19 would be = Number of paper pieces with Number 19/Total number of pieces of paper with an odd number = 1/12

We take only the pieces of paper with an odd number on it as we already know the student is in the blue team so they had to have an odd number.

After reading quote from chapters 1-3 of Treasure Island.

"He cleared the hilt of his cutlass and loosened the blade in the sheath; and all the time we were waiting there he kept swallowing as if he felt what we used to call a lump in the throat."

Based on the actions described in the quote, Black Dog is feeling fear. Hence option B is correct answer.

Clearing the hilt of his cutlass and loosening the blade in the sheath are actions typically taken when one is preparing for potential danger or conflict.

Therefore, based on the above, the fact that Black Dog is swallowing as if he has a lump in his throat is another indication that he is feeling fear or nervousness.

Correct option is: B

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Answer:

MAGNITUDE AND DIRECTION OF A VECTOR

Given a position vector →v=⟨a,b⟩,the magnitude is found by |v|=√a2+b2. The direction is equal to the angle formed with the x-axis, or with the y-axis, depending on the application. For a position vector, the direction is found by tanθ=(ba)⇒θ=tan−1(ba)

Step-by-step explanation:

Answer: The 2013-2014 salary can be calculated as follows:

$483,000 + ($483,000 * 3.1%) = $483,000 + $14,973 = $497,973.

So, the university president's 2013-2014 salary was approximately $497,973 after receiving a 3.1% raise.

Step-by-step explanation:

The fraction of all the animals that are not dogs and cats is 9/40 or 0.225.

The fractions of the dog and cat populations are summed and subtracted from 1, which represents the total population of the animals.

The fractions can also be expressed as decimals using division operations.  They can also be depicted in percentages by multiplying the division quotients by 100.

Fractions of Animal Populations in the Shelter:

Dogs = 2/5

Cats = 3/8

2/5 + 3/8 = 31/40

The lowest common factor of 5 and 8 is 40.

Other pets = x

x = (1 - 31/40)

x = 9/40

Thus, since 2/5 of the animal populations are dogs and 3/8 are cats, the rest of the pets, including birds, hamsters, and lizards can be represented fractionally as 9/40.

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Mean = 31.333

Median = 30

Mode = 41

Range = 18

Mean

Determining the average can be done by adding up all the data values, then dividing by the amount of data.

Mean = [tex]\frac{30+25+23+41+39+27+41+24+32}{9}[/tex]

         = [tex]\frac{282}{9}[/tex]

         = 31.333

Median

The median is the middle value of a set of data after being sorted from smallest to largest data, and vice versa. If data has a median, then the median is single.

because the questions are not sequential, they must be sorted first from the smallest to the largest.

23 24 25 27 30 32 39 41 41

The median from this question is 30

Mode

The mode is the data that occurs most frequently.

23 24 25 27 30 32 39 41 41

And the mode of this problem is 41 because it appears two times

Range

the range is the difference between the highest value of a data set and the lowest value of a data set.

23 24 25 27 30 32 39 41 41

the range from 23 to 41 is 18

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Answer:

89/100

Step-by-step explanation:

there were only 11 people without treatment so minus 11 from 100 which is 89

then just make it a probability by writing it out of 100.

hope this helps

Answer:

S(x) = 3 × 2^x

Step-by-step explanation:

it is an exponential sequence

the common ratio is 2

To convert a point from Cartesian coordinates to cylindrical coordinates, use the formulae:

r²=x²+y² ,

tanθ=y/x, and z=z

What are coordinates?

A pair of numbers that use the separations between the two reference axes to define the location of a point on a coordinate plane. usually represented by the x- and y-values, respectively, (x, y).

The position of a point or a shape in a given space is determined by coordinates, which are numbers (a map or a graph ).

To convert a point from Cartesian coordinates to cylindrical coordinates, use the formulae:

r²=x²+y² ,

tanθ=y/x, and z=z

Cartesian coordinates are also called as rectangular coordinates

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To convert a point from Cartesian coordinates to cylindrical coordinates, use the formulae:

r²=x²+y² ,

tanθ=y/x, and z=z

What are coordinates?

A pair of numbers that use the separations between the two reference axes to define the location of a point on a coordinate plane. usually represented by the x- and y-values, respectively, (x, y).

The position of a point or a shape in a given space is determined by coordinates, which are numbers (a map or a graph ).

To convert a point from Cartesian coordinates to cylindrical coordinates, use the formulae:

r²=x²+y² ,

tanθ=y/x, and z=z

Cartesian coordinates are also called as rectangular coordinates

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Answer:

Step-by-step explanation:

Polk Elementary School was putting on its annual fall carnival. The school was selling 10 tickets for $1.00 or 2 tickets for 254. Which is the better buy? Explain why.

Therefore , the solution of the given problem of expression comes out to be its final simplification is 5ln4y - 2lnx.

There is a need for mathematical operations such addition, multiplication, multiplication, and division. When variable combined, they produce the following: A mathematical operator, some data, and an equation A statement of fact is composed of values, parameters, plus operations like additions, subtractions, multiplications, and divisions. It is possible to contrast and compare various sentences and words.

Here,

Given :

To expand the given expression :

=> ln [ (4y)⁵/ x² ]  

=> ln [ (4y)⁵/ x² ]  

=> ln(4y)⁵ - lnx²

=> 5ln4y - 2lnx

Thus,

its final simplification is : 5ln4y - 2lnx.

Therefore , the solution of the given problem of expression comes out to be its final simplification is 5ln4y - 2lnx.

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Answer:

w = (10√3)/3

x = 5

y = 5√2

z = (5√3)/3

Step-by-step explanation:

→ The length of "x" is also 5 units because 45-45-90 triangles have the same leg lengths.

→ The length of "y" is 5√2 units because the hypotenuse of a 45-45-90 triangle is √2 times bigger than either leg length.

→ The length of "z" is 5/√3 or (5√3)/3 units because the longer leg length of a 30-60-90 triangle is √3 times bigger than the shorter leg length

→ The length of "w" is (10√3)/3 units because the longer leg length is 2 times bigger than the shorter leg length of a 30-60-90 triangle

See below for more information about general rules for 30-60-90 and 45-45-90 triangles!

Answer: £2,116.10 each month.

Step-by-step explanation:

To calculate the monthly payment, we first need to find the total amount owed after the compound interest has been added. The formula for compound interest is:

A = P * (1 + r/n)^(nt)

where:

A is the amount owed,

P is the initial principal (the cost of the tractor),

r is the annual interest rate,

n is the number of times interest is compounded per year, and

t is the number of years the loan is taken out for.

In this case:

P = £64,950

r = 4% = 0.04

n = 12 (the number of months in a year)

t = 3 (the number of years the loan is taken out for)

Plugging these values into the formula, we find that:

A = £64,950 * (1 + 0.04/12)^(12*3) = £76,079.69

To find the monthly payment, we divide the total amount owed by the number of payments:

Monthly payment = A / 36 = £76,079.69 / 36 = £2,116.10

So you will pay £2,116.10 each month.

Answer: $180

Step-by-step explanation:

180 x 15% = 27
27 - 180 = 153

Given a discount rate of 0.15, the NPV of these financial movements is therefore $378.73.

Spending that occurs in the normal run of business is included in cash flow from activities. Payroll, the cost of products sold, rent, and utility bills are a few examples of these cash withdrawals. When company activities are extremely seasonal, cash outflows can differ greatly.

Here's how to do the calculation:

We need to determine how many days passed between the first monetary influx of $-1000, which was received on 12/15/2021, and the present day (2/21/2023). It's been 432 days. Using the equation PV = FV / (1 + r)n, we can determine the current value (PV), the future value (FV), the discount rate (r), and the number of times (n). When the numbers are plugged in, we get PV = -1000 / (1 + 0.15)(432/365) = -845.67.

We must determine how many days passed between the second monetary influx of $300, which was received on January 11, 2022. It's been 406 days. We obtain PV = 300 / (1 + 0.15)(406/365) = 246.87 using the same method.

In order to determine the third financial movement, which is a $600 payment received on 4/7/2023, we must determine how many days have passed since that date. It's been 410 days. Using the same method, we get PV = 600 / (1 + 0.15)^(410/365) = 427.81.

We need to figure out how many days passed between the fourth financial transfer, which was $925 and was received on July 15, 2024. It has been 875 days. We obtain PV = 925 / (1 + 0.15)(875/365) = 548.72 using the same method.

Now we can add up the present values of all the cash flows to obtain the NPV:

NPV = -845.67 + 246.87 + 427.81 + 548.72 = 378.73

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Kara's grandmother knitted the cap during the afternoon is [tex]\frac{1}{2}[/tex].

A fraction is a number that represents the part of a whole. It is in the form of [tex]\frac{a}{b}[/tex] , in which upper 'a' part denotes numerator and the lower part 'b' denotes the numerator.

Kara's grandmother knitted the cap,

In the morning = [tex]\frac{1}{5}[/tex]

In the evening = [tex]\frac{7}{10}[/tex]

She knitted during the afternoon = [tex]\frac{7}{10} -\frac{1}{5}[/tex]

                                                       = [tex]\frac{7}{10} - \frac{2}{10}[/tex]

                                                       = [tex]\frac{5}{10} = \frac{1}{2}[/tex]

Hence, Sara's grandmother knitted the cap during the afternoon =[tex]\frac{1}{2}[/tex].

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the data classification (categorical or quantitative) and type of data (Nominal or Ordinal or Continuous or Discrete)

A. Height of sunflowers in a field.

1.Quantitative

2.Continuous

B. Jersey color of all the NCAA football teams.

1.Categorical

2.Nominal

A. Height of sunflowers in a field.

1.Quantitative

2.Continuous

B. Jersey color of all the NCAA football teams.

1.Categorical

2.Nominal

Data classification is a process of organizing data into categories based on their characteristics, attributes, or features. There are two main types of data classification:

Categorical Data: Data that can be divided into categories or classes. For example, color, gender, and type of cuisine are all examples of categorical data. Categorical data can be further classified into two types:

a. Nominal Data: Data that does not have an inherent order or ranking. For example, hair color, eye color, and favorite movie are all examples of nominal data.

b. Ordinal Data: Data that has a natural order or ranking. For example, education level (high school, college, postgraduate), star rating (1 star, 2 stars, 3 stars), and satisfaction level (very unsatisfied, unsatisfied, neutral, satisfied, very satisfied) are all examples of ordinal data.

Quantitative Data: Data that can be measured and expressed as a number. For example, height, weight, and time are all examples of quantitative data. Quantitative data can be further classified into two types:

a. Continuous Data: Data that can take on any value within a specified range. For example, height, weight, and temperature are all examples of continuous data.

b. Discrete Data: Data that can only take on specific values. For example, number of children in a family, number of pets, and number of rooms in a house are all examples of discrete data

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