Tom is leading a workshop for 15 people. He wants each person to meet every other person (shake hands once). How many handshakes occur?

Step-by-step explanation:

Set each binomial equal to 0, solve for x.

[tex](x + 5) = 0[/tex]

[tex]x = - 5[/tex]

[tex](x - 2) {}^{2} = 0[/tex]

[tex]x - 2 = 0[/tex]

[tex]x = 2[/tex]

The zeroes are -5, and 2(with a multiplicity of 2)

We have a degree of 3.

[tex](x + 5)(x {}^{2} - 4x + 4)[/tex]

the first term in each binomail when using FOIL, become x^3 since that is the highest degree, 3 is the degree of c.

Answer:

The above answers are incorrect.

Step-by-step explanation:

If the price of one of the goods decreases, the quantity demanded of that good will increase due to the substitution effect. This means that the consumer will choose to buy more of the cheaper good and less of the more expensive good. The income effect may also come into play, as the consumer now has more disposable income due to the lower price of one of the goods. However, it is not possible to determine the exact quantity of each good that the consumer will purchase without further information.

In this case, if the price of one of the goods decreases from $10 to $8, the consumer will likely purchase more of that good and less of the other good, which is a substitution effect. The income effect may also come into play, as the consumer now has more disposable income due to the lower price of one of the goods. However, it is not possible to determine the exact quantity of each good that the consumer will purchase without further information.

Therefore, the correct answer is e. The above answers are incorrect.

The number of routes that Paula can take using graph theory is; E: 4

We will observe that out of the 12 cities, 6 of them possess 3 edges going in/out of them.

The 6 cities are such that there are 2 at the top, 2 at the bottom, and 1 on each side.

In graph theory terms, we can say that they are of degree 3.

Thus, at least 1 edge connecting to each of these cities cannot therefore be used. Furthermore, the same concept applies to the start and end points, due to the fact that we don't want to return to them.

There are 6 + 2 = 8 vertices that we can tell have 1 unused edge, and then we have 17 - 13 = 4 unused edges to work with due to the fact that we have 17 edges in total, and as such must use exactly 13 of them).

Finally, we notice that at each of the 2 cities marked with an O on a path in the image attached, that there are 2 possibilities such that it's either we continue straight and cross back over that same path later, or we will make a left turn, and then turn rightward when we approach the junction again.

This gives us a total of;

2 * 2 = 4 possible different routes

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The one poison dart frog is 1/4 inch longer than the other.

What is Poison dart frog?

A family of frogs known as the Dendrobatidea that are indigenous to tropical Central and South America go by the common name "poison dart frog." These species are nocturnal and frequently have colorful bodies. These aposematic species have a bright coloration that is linked to the species' toxicity.

Given: Mary saw two poison dart frogs.

One was 7/8 inch long and the other was 5/8 inch long.

So, 7/8 - 5/8 = 2/8 = 1/4

Hence, the one poison dart frog is 1/4 inch longer than the other.

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The given statement is false. If a sample is selected using random sampling methods, the primary reason that the sample mean might be different from the corresponding population mean is not that the sample might be biased.

Because random sampling ensures that results obtained from the sample should approximate what would have been obtained if the entire population had been measured. And the simplest random sample allows all the units in the population to have an equal chance of being selected. In this case, the sample might not be biased.

Random sampling is a part of the sampling technique where each sample has an equal probability of being chosen. A sample chosen randomly is meant to be an unbiased representation of the total population.

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The amount in his savings after 5 years will be  $1507.5.

We know simple interest (SI) is given by SI = (p×r×t)/100, where

p = principle, r = rate in percentage, and t = time in years.

Given, P = 1500, r = 0.1, t = 5 years.

∴ SI = (1500×0.1×5)/100.

SI = $7.5.

Now, We know Amount = principle + SI.

∴ Amount = 1500 + 7.5 = $1507.5

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2,200 caterpillars are expected to become a butterfly in 17.8 days or more.

Formula: Z= (x-bar-mean)/σ: where x-bar is the score to which we are calculating a Z value; mean is just the arithmetic mean of the sample or population, and σ is the standard deviation of the sample or the population. Check attached image 1 below.

Substitute and calculate:

[tex]Z=(17.8-15)/3.5\\\\ Z=0.8[/tex]

For this solution, we are going to b e using Microsoft Excel's tools to calculate the probabilities. Check attached image 2.

[tex]IP(Z\leq 17.8)=0.7881[/tex]

This is the probability that any caterpillar becomes a butterfly in 17.8 days or less. This is how Microsoft Excel calculates probabilities for default. Now, in order to get the probability that the problem asks for (17.8 days or more) we just need to do the following operation:

[tex]1-0.778=0.222[/tex]

[tex](0.222)(10,000)=2,220[/tex]

2,200 caterpillars are expected to become a butterfly in 17.8 days or more.

Answer: y = 11x + 31, the y - intercept is 31!

Step-by-step explanation:

The equation that models this situation is y = mx + b

We already have the slope, m, of 11.

since we have 2 coordinates, we can substitute all the known values into the equation.

==> 108 = 11 (7) + b

Multiply.

==> 108 = 77 + b

Take 77 from both sides

==> 108 - 77 = 77 - 77 + b

==> 31 = b

==> This means that the y intercept of this linear function is;

f(x) = 11x + 31

or

y = 11x + 31

By using the concept of function, it can be calculated that-

a) [tex]\frac{g}{f}(-4) = \frac{4}{31}[/tex]

b) The point [tex]\frac{7}{6}[/tex] is not in the domain of [tex]\frac{g}{f}[/tex]

What is a function?

A function from A to B is a rule that assigns to each element of A a unique element of B. A is called the domain of the function and B is called the codomain of the function.

There are different operations on functions like addition, subtraction, multiplication, division and composition of functions.

Here,

a) The given functions are -

   g(x) = (x + 6)(x  + 6)

  f(x)= -6x+7

   [tex]\frac{g}{f}(x) = \frac{g(x)}{f(x)} = \frac{(x+6)(x+6)}{-6x+ 7} = \frac{(x+6)^2}{-6x + 7}[/tex]

   [tex]\frac{g}{f}(-4) = \frac{g(-4)}{f(-4)} = \frac{(-4+6)^2}{-6(-4) + 7} = \frac{4}{31}[/tex]

b)  [tex]\frac{g}{f}(x)[/tex] is not defined if -6x + 7 = 0

     [tex]\frac{g}{f}(x)[/tex] is not defined if  [tex]x = \frac{7}{6}[/tex]

      So the point [tex]\frac{7}{6}[/tex] is not in the domain of [tex]\frac{g}{f}[/tex].

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Fe^2 + → Fe^3 + + e^- is an example of oxidation

How many oxidations do Fe3+ and Fe2+ ions have?

For instance, the oxygen ion O2+ has an oxidation number of 2 because it can contribute two electrons, whereas the iron ion Fe3+ has an oxidation number of +3 because it can take on three electrons to establish a chemical bond.

[tex]$\mathrm{Fe}_3 \mathrm{O}_4$[/tex] contains [tex]$\mathrm{F}$ e[/tex] atoms of both[tex]$+2$ and $+3$[/tex]oxidation number.

It is a stoichiometric mixture of[tex]Ferrous $(\mathrm{FeO})$[/tex]

and Ferric [tex]$\left(\mathrm{Fe}_2 \mathrm{O}_3\right)$ oxides combined as $\mathrm{FeO} \cdot \mathrm{Fe}_2 \mathrm{O}_3$.[/tex]

[tex]Oxidation state of oxygen in $\mathrm{FeO}$ and $\mathrm{Fe}_2 \mathrm{O}_3$ is $-2$.[/tex]Let the oxidation state of [tex]$\mathrm{Fe}$ in $\mathrm{FeO}$ and $\mathrm{Fe}_2 \mathrm{O}_3$ be $\mathrm{x}$ and $y$[/tex]

As we know that the sum of the oxidation states of all the atoms or ions in a neutral compound is zero.

ThereforeOxidation state of [tex]$\mathrm{F}$ e in $\mathrm{F}$ eO-[/tex]

&[tex]x+(-2)=0 \\& \Rightarrow x=2[/tex]

Oxidation state of[tex]$\mathrm{F}$ e in $\mathrm{Fe}_2 \mathrm{O}_3-$[/tex]

&[tex]2(\mathrm{y})+3(-2)=0 \\& \Rightarrow 2 \mathrm{y}=6 \\& \Rightarrow \mathrm{y}=3\end{aligned}[/tex]

Hence the oxidation number of [tex]$\mathrm{Fe}$ in $\mathrm{Fe}_3 \mathrm{O}_4$ are $+2$ and $+3$[/tex]respectively.

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The number written as a fraction in simplest form is 4/5

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

Clausometer = 80%

Turn the percentage to fraction

So, we have the following representation

Clausometer = 80/100

Divide 80 and 100 by 10

So, we have the following representation

Clausometer = 8/10

Divide 8 and 10 by 2

So, we have the following representation

Clausometer = 4/5

Hence, the fraction is 4/5

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Answer:

(1,2) and (4,2)

(2,6) and (6,6)

Step-by-step explanation:

(when a line is horizontal the slope is 0)

[tex]slope = \frac{rise}{run} [/tex]

[tex]rise = y1 - y2[/tex]

[tex] = 2 - 2 \\ = 0[/tex]

[tex]run = x2 - x1 \\ = 4 - 1 \\ = 3[/tex]

[tex]slope = \frac{0}{3} \\ = 0[/tex]

second option

[tex]rise = 6 - 6 \\ = 0[/tex]

run=6-2

=4

slope= 0/4

=0

please Heart this....

Using some mathematical operations, we know that the total cost of the fencing will be $737 approximately.

An operation is a function in mathematics that transforms zero or more input values into a clearly defined output value.

The operation's arity is determined by the number of operands.

Mathematical operations include addition, subtraction, multiplication, division, and finding the root.

So, the total cost of fencing is:

According to the given figure, the total length of fencing will be:

8m + 8m + 6m + 2m + 2m + 6m

32 m

Now, 4% more of the total fence:

4/32 * 100

1.28 m

Now the total fencing length:

32 + 1.28

33.28 m

We know that:
1m = 3.2 ft

33.28m = 109.18 ft

We are given that fencing of 4 feet costs: $27. Then,

109.18/4

27.295 * $27

$736.965

Rounding off: $737 approximately

Therefore, using some mathematical operations, we know that the total cost of the fencing will be $737 approximately.

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The money will double in value in approximately 11.6 years.

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

When the money doubles, the amount is

A = 900 * 2

A = 1800

The compound interest formula is given as

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

Also from the question, we have

n = 12

This is so because the loan is compounded 12 times in a year as a result of being compounded monthly

Solving further, we replace the variables with their values in the above equation

1800 = 900 * (1 + (6%)/12)^(t*12)

Divide both sides by 900

2 = (1 + (6%)/12)^(t*12)

Also, we have

2 = (1.005)^(t*12)

Take the logarithm of both sides

12t = log(2)/log(1.005)

Evaluate the quotients

12t = 139

Divide both sides by 12

t = 11.6

Hence, the number of years is 11.6 years

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The solution set for the inequality - x < 2 is - x < 2.

What is  inequality?

In mathematics, inequalities specify the connection between two non-equal numbers. Equal does not imply inequality. Typically, we use the "not equal sign ()" to indicate that two values are not equal. But several inequalities are utilized to compare the numbers, whether it is less than or higher than.

An inequality in mathematics depicts the connection between two values in an unbalanced algebraic statement. A sign of inequality can be used to show that one of the two variables is larger than, more than or equal to, less than, or equal to another value.

-x<2

Multiply both sides by -1 (reverse the inequality)

(-x)(-1)>2(-1)

Simplify

x>-2

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w is less than 75.

What do you mean by algebraic expression?

An expression constructed using integer constants, variables, and algebraic operations is known as an algebraic expression (addition, subtraction, multiplication, division and exponentiation by an exponent that is a rational number)

An equation that only uses algebraic expressions is known as an algebraic equation.

Any mathematical operation that involves variables, such as addition, subtraction, multiplication, or division, can have its solutions calculated using algebraic expressions.

Given expression:

[tex]\frac{75}{w}=\frac{150}{100}[/tex]

⇒ w = [tex]\frac{75 \times 100}{150 }[/tex]

⇒ w = 50

Convert the value of w into percentage.

w = 50 × 100 % = 500%

Therefore, w is less than 75.

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The required equation of conic section that shows eclipse is  [tex]\frac{(x-2)^2}{4^2} + \frac{(y-4)^2}{6^2}=1[/tex].

An equation is a combination of different variables, in which two mathematical expressions are equal to each other.

Let the standard equation of conic section,

[tex]\frac{(x-h)^2}{a^2} + \frac{(y-k)^2}{b^2}=1[/tex]      (1)

From the given diagram,

The center of the eclipse is (2, 4),

Here h = 2, and k = 4

The length of minor axis 2a = 8 ⇒ a = 4

The length of major axis 2b = 12  ⇒ b = 6

Substitute the values of a, b and h, k in equation (1)

[tex]\frac{(x-2)^2}{4^2} + \frac{(y-4)^2}{6^2}=1[/tex]

The required equation of the given conic section is [tex]\frac{(x-2)^2}{4^2} + \frac{(y-4)^2}{6^2}=1[/tex].

The conic section represents the eclipse.

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Answer:

1

Step-by-step explanation:

anything to the power of 0 is 1

hopes this helps

8,9,10 is the value from the given replacement set make-up the solution set for inequality.

In mathematics if a statement of an order relation greater or greatest then or equal to is called inequality. To compute the inequality:

if we replace m with 8 it will be 8+7 which is 15 and less then 18

for 9 its 9+7 which is 16 which is less then 18

and for 10 its 10+7 which is 17 which is less then 18

and for 11 its 11+7 is 18 which is equal to 18 so it would not apply to this equation.

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The proportional relationship of the table are as follows:

Proportional relationships are relationships between two variables where their ratios are equivalent.

A proportional relationship is one in which two quantities vary directly with each other. We say the variable y varies directly as x if:  

y = k x

for some constant k , called the constant of proportionality.

First table

k =hx

10 = 2x

x = 5

Hence,

k = 5h

h = 1 / 5 k

Second table

k = hx

5 = 4x

x = 5 / 4

Hence,

k = 5 / 4 h

Third table

k = hx

5 = 25x

x = 5 / 25

Hence,

k = 1 / 5 h

h = 5k

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This bolt should go into the package. The percentage of error is 2.22% which is less than 3%.

What is the meaning of error?

The discrepancy between a variable's observed value and its actual but unseen value

Given that the diameter of each bolt is 0.45 inch.

The percentage of error the diameter of each bolt must be less than 3%.

A bolt picks for a test. The diameter of the bolt is 0.46 inch.

The formula of percent error is

The difference of the diameters/ the original diameter of bolt )× 100%

= [(0.46 - 0.45)/0.45] × 100%

= (0.1/0.45) × 100%

= 0.0222 × 100%

= 2.22%

The percentage of error is less than 3%. So the lot is good to go.

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Answer:

look below

Step-by-step explanation:

To determine the upper-tail critical value of the test statistic for a chi-square test for independence in a contingency table, you can use a table of critical values for the chi-square distribution or you can use a statistical software package or calculator to compute the critical value.

In each of the following circumstances:

a. a=0.05, r=3, c=4: The critical value would be the upper-tail critical value of the chi-square distribution with 3 degrees of freedom and an alpha level of 0.05.

b. a=0.01, r=5, c=6: The critical value would be the upper-tail critical value of the chi-square distribution with 5 degrees of freedom and an alpha level of 0.01.

c. a=0.01, r=5, c=4: The critical value would be the upper-tail critical value of the chi-square distribution with 5 degrees of freedom and an alpha level of 0.01.

d. a=0.01, r=3, c=4: The critical value would be the upper-tail critical value of the chi-square distribution with 3 degrees of freedom and an alpha level of 0.01.

e. α=0.01, r=6, c=5: The critical value would be the upper-tail critical value of the chi-square distribution with 6 degrees of freedom and an alpha level of 0.01.

It's important to note that the critical value is dependent on the degrees of freedom and the alpha level, so you will need to use the appropriate values for these parameters in order to determine the correct critical value.

The coordinates to plot the graph after solving the equation will be 0.33 and 1.2.

In math, graph science is the theory of geometric structures called graphs that are used to represent pairwise different objects. Vertices—also known as nodes or points—that are joined by edges make form a network in this sense.

Undirected graphs, where edges connect two vertices equally, and focused therapy, where edges connect two vertices unevenly, are distinguished.

As per the given expressions to plot, the graph is,

f(x) = 3x - 1 and,  (i)

h(x) = -4x - 5       (ii)

From equation (i),

f(x) = 3x - 1

3x = 1

x = 1/3

x = 0.33

From equation (ii)

h(x) = -4x - 5

-4x = 5

x = -5/4

x = 1.2

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The distance between the bank and Hiroto's house on the map is 11.5 units.

A coordinate plane is a 2D plane that is formed by the intersection of two perpendicular lines known as the x-axis and y-axis. A coordinate system in geometry is a method for determining the positions of the points by using one or more numbers or coordinates.

The distance between the bank and Hiroto's house will be calculated as,

The coordinates are, B(-8,6) and H(3.5,6).

D=√(3.5-(-8))²+(6-6)²

D = √11.5²

D = 11.5

Therefore, the distance between the bank and Hiroto's house on the map is 11.5 units.

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That is a geometric progression.

the common ratio is 1/2.(t2÷t1)

nth term= ar^n-1

16×1/2=8

tn=8^n-1

The average amount that the roller coaster's height drops over each horizontal foot will be -5 feet.

The four basic mathematical operations are the addition, subtraction, multiplication, and division of two or even more integers. Among them is the examination of integers, particularly the order of actions, which is crucial for all other mathematical topics, including algebra, data organization, and geometry.

As per the given data in the question,

Slope = change in y/change in x

Slope = Δy/Δx

A 20-foot horizontal drop is present on a roller coaster.

So, Δx = 20-foot

The roller coaster is 100 feet tall when it is at the bottom of the drop.

So, Δy = -100 feet.

Now, the average rate of change will be,

= -100/20

= -5/1 = -5

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The error student made was converting 6.5% to decimal

6.5% = 0.065

0.065 * 525.08 =  $34.13

information from the problem

A student is finding a 6.5% commission on $525.08 worth of sales

The question is a percentage problem, percentage deals with a fraction hundred and used as follows

6.5%

=  6.5 percent

= 6.5 / 100

= 0.065

The factor 0.065 of the commission on $525.08

= 0.065 * 525.08

= $34.13

The commission is $34.13

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a) The percentage of buyers that paid between $18,000 and $26,000 is; 95%

b) The middle 99.7% of car costs are between $16000 and $28000

c) The probability a car will cost less than $24,000 is; 68%

d) The probability a car will cost more than $26,000 is; 2.5%

The empirical rule of statistics states that 68% of data will be ± 1 standard deviations from the mean, 95% of data will be ± 2 standard deviations of the mean, and 99.7% of data will be ± 3 standard deviations from the mean.

a) We are given;

Mean; μ = $22000

Standard deviation; σ = $2000

$18,000 and $26,000 are both 2 standard deviations from the mean and so, the percentage of buyers is 95%.

b) Since the middle 99.7% of car costs, this is simply 3 standard deviations from the mean and as such it is between the values;

22000 - 3(2000) = $16000 and 22000 + 3(2000) = $28000

c) $24,000 is 1 standard deviation away from the mean and as such the probability will be 68% from empirical rule.

d) $26000 is 2 standard deviations from the mean and as such probability that a car will cost more than that is;

(100% - 95%)/2 = 5%/2 = 2.5%

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