(b) Prove that the points (0, 0), (1, 0), (1, 1), and (0, 1) are the vertices of a
unit square. Also plot the square on graph paper.

The linear function which represents the line is y = - 3x + 14.

What is Point slope form?

Point slope form is used to represent a straight line using its slope and a point on the line. It means that the equation of a line whose slope is 'm' and which passes through a point (x1, y1) is found using the point-slope form.

Main body:

y - y1 = m (x - x1)

where, (x, y) is a random point on the line and m is the slope of the line.

The given point-slope equation is

y + 1 = - 3 (x - 5)

By further calculation

y + 1 = -3x + 15

y = -3x + 15 - 1

y = -3x + 14

Therefore, the linear function which represents the line is y = - 3x + 14.

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CuBr is soluble in pure water at a solubility of 0.2583 g/L, while CoBr₂ is soluble at a solubility of 7.50 × 10⁻⁶ g/L

Given,

The equation of reaction as; CuBr₂ → Cu²⁺ + 2Br⁻

In pure water, the Ksp of the solution is 6.27 * 10^-9

Ksp = [Cu²⁺] [Br⁻]²

Ksp = x³

Let's substitute and solve

x³ = 6.27 × 10⁻⁹

x = [tex]\sqrt[3]{6.27 * 10^{-9} }[/tex]

x = 0.0018

The molecular weight of CuBr₂ is 143.5 g/mol

The solubility of CuBr₂ is

0.0018 × 143.5 = 0.2583 g/L

The solubility in 0.0060M of CoBr₂

The equation of dissociation is given as

CoBr₂ → Co²⁺ + 2Br⁻

0.012         0         0

0                0.120   2 * 0.0060 = 0.012M

The dissociation of copper bromide is

CuBr₂ → Cu²⁺ + Br⁻

c                 0         0.012

c - s             s          s + 0.012

The Ksp of this reaction is

[Ksp] = [Co²⁺] [Br⁻]

The Ksp of CuBr₂ = 6.27 × 10⁻⁹

6.27 × 10⁻⁹ = s(s + 0.012)

s + 0.012 = 0.012

0.012 > > > s

6.27 × 10⁻⁹ = s × 0.012

s = 6.27 × 10⁻⁹ / 0.012 = 5.225 × 10⁻⁷ mol / l

Let's convert this into g/L

s =  5.225 × 10⁻⁷ × 143.5 = 7.50 × 10⁻⁶ g/L

Therefore,

The solubility of CuBr in pure water is 0.2583 g/L and the solubility in CoBr₂ is 7.50 × 10⁻⁶ g/L

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The elements of a treaty includes, satisfaction of both sides, a proper set of rules and obligation towards the actions.

By the definition are Treaty is a diplomatic agreement between two countries on global issues.

According to the constitution of The United States of America the president of the state can make the treaty with other countries with the support of the two third of the sinters present in the house as per the section 2 of Article II.

An agreement can only be called a Treaty if the agreement is agreed upon by both the sides and the Treaty has a proper set of rules define for both the countries and both the countries give their consent towards their actions which comes under the treaty.

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The triengle ABC and XZY are proved to be congruent by SAS.

Congruence of triangles: Two triangles are supposed to be harmonious assuming each of the three comparing sides are equivalent and every one of the three relating angle are equivalent in measure. These triangles can be slides, pivoted, flipped and went to be seemed to be indistinguishable.

By the rule of SAS which means, Two sides are equal thhen the angle between the two sides is also equal (SAS: side, angle, side)

Here in he given triangle,

BC=YZ

AC=XZ

∠ACB=∠XZY

By SAS ΔABC≅ΔXYZ

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The simplified form of the expression, (4x3 + 6x) + (5x3 + x), is 9x³ + 7

From the question, we are to add and simplify the given expression.

The given expression is

(4x3 + 6x) + (5x3 + x)

First, we will write the given expression properly.

The given expression written properly is

(4x³ + 6x) + (5x³ + x)

Now, we will simplify the expression by adding the like terms

Simplifying the expression

(4x³ + 6x) + (5x³ + x)

Collect like term s

4x³ + 5x³ + 6x + x

Simplify the expression by adding up the like terms

9x³ + 7x

Hence, the simplified expression is 9x³ + 7x

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Using the addition and subtraction operations, we find out that the money left with Camillo is equal to $361.75.

It is given to us that -

The total cost for bread = $48.75

The total cost for peanut butter = $384

and, the total cost for jelly = $192

It is also given to us that Camillo has spent $986. 50.

We have to find out the money he has left.

Firstly, we have to find out the total costs spent by Camillo by adding the costs spent on bread, peanut butter, and jelly.

Total costs = $48.75 + $384 + $192 = $624.75

The total amount that Camillo had with him initially is given by $986. 50.

So, in order to find out the money that Camillo is left with, we have to subtract the total costs spent by Camillo from the initial total amount that Camillo had.

Thus, money left = $986. 50 - $624.75 = $361.75

Therefore using addition and subtraction operations, we find out that the money left with Camillo is equal to $361.75.

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Answer: Camillo had  $361.75.

Step-by-step explanation:

Answer:

[tex]4\frac{1}{2}[/tex] or [tex]\frac{9}{2}[/tex]

Step-by-step explanation:

1. 0.5 means a half of 1  so it would be equivalent to [tex]\frac{1}{2}[/tex]

2. 4 in this case equals to [tex]\frac{8}{2}[/tex]

3. if you add them together you would get [tex]\frac{9}{2}[/tex]

4. after simplifying you would get [tex]4\frac{1}{2}[/tex]

5. so in this case both [tex]\frac{9}{2}[/tex] and [tex]4\frac{1}{2}[/tex] would be the answer

Answer:6 times

Step-by-step explanation:12/7 divide 1/4

Answer:  6  times

Step-by-step explanation:  

The probability that suits of cards are spades, hearts, and spades is 39/850 or 0.046.

According to the give question.

Three cards are drawn from a standard deck of cards without replacement.

Since,

The total number of cards in a standard deck = 52

Total number of spade cards = 13

Total number of heart cards = 13

Now,

The probability of getting first card as a spade card = 13/52 = 1/4

The probability of getting second card as heart card = 13/(52 -1)     (cards are drawn without replacement)

                                                                                        = 13/51

The probability of getting third card as a spade card = (13 - 1)/52 -2

                                                                                        = 12/50

                                                                                        = 6/25

Therefore, the probability that suits of the cards are spades, hearts, spades

= 1/4 × 13/51 × 6/25

= 39/850

= 0.046

Hence, the probability that suits of cards are spades, hearts, and spades is 39/850 or 0.046.

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Answer:

67

Step-by-step explanation:

Let x be the first integer.

Therefore, the six consecutive integers are:

If the sum of the six consecutive integers is 387 then:

⇒ x + x + 1 + x + 2 + x + 3 + x + 4 + x + 5 = 387

⇒ 6x + 15 = 387

⇒ 6x + 15 - 15 = 387 - 15

⇒ 6x = 372

⇒ 6x ÷ 6 = 372 ÷ 6

⇒ x = 62

To find the sixth number, substitute the found value of x into the expression for the sixth number:

⇒ x + 5 = 62 + 5 = 67

After solving the equation, x=6 so the solution is extraneous.

In the given question, the equation square root of quantity 3x minus 2 end quantity equals 4.

We have to solve for x and identify if it is an extraneous solution.

A root of a converted equation that is not a root of the original equation because it was left out of the original equation's domain is referred to as a superfluous solution.

Now the equation is

√3x-2 = 4

Taking square on both side, we get

3x-2 = 16

Add 2 on both side, we get

3x = 18

Divide by 3 on both side, we get

x = 6

Hence, x=6 so the solution is extraneous.

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The type of chart that would work best to show a comparison between the number of cable and satellite TV subscribers is bar chart.

A bar chart or bar graph is a chart or graph that conveys categorical data with rectangular bars with heights or lengths proportional to the values which they represent. The bars may be plotted vertically or horizontally. A vertical bar chart is also called a column chart.

A bar chart is used when we want to show a distribution of data points or present a comparison of metric values between different subgroups of our data. From a bar chart, we can preview which groups are the highest or most common, and how the other groups compare to the others.

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We can extend our definition of the average value over a continuous function to an infinite interval by defining the average value f on the interval [0, ∞) to be      [tex]\lim_{t \to \infty}\frac{1}{t-a}\int\limits^t_a {f(x)\\} \, dx[/tex]  .

The definition of the average value of a continuous function f(x) can be expanded to include the infinitely long interval [a,∞] as follows:

[tex]\lim_{t \to \infty}\frac{1}{t-a}\int\limits^t_a {f(x)\\} \, dx[/tex]

Let's assume that f(x) is any continuous function. Assume that the integral [tex]\int\limits^i_0 {f(x)} \, dx[/tex]   is divergent and that f(x)≥0 in the range [a,∞].

Show that, if this limit exists, [tex]f_{ave} = \lim_{x \to \infty} f(x)[/tex] .

Hence, We can extend our definition of the average value over a continuous function to an infinite interval by defining the average value f on the interval [0, ∞) to be      [tex]\lim_{t \to \infty}\frac{1}{t-a}\int\limits^t_a {f(x)\\} \, dx[/tex]  .

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The amount of  grape juice that you need to mix with 15 over 4 quarts of sparkling water is 15/8 quarts

Given that,

The amount of Sparkling water is 15/4 quarters

To find : The amount of grape juice that you need to mix with 15 over 4 quarts of sparkling water

Sparkling water measuring 1 1/2 quarters is required for the recipe. This can be expressed as the improper fraction 3/2 (since 1 whole equals 2/2 and 2/2 plus 1/2 equals 3/2).

We used 5/2 times as much sparkling water as the recipe called for, or 15/4 quarts (15/4 gallons). This implies that we would also use 5/2 times as much grape juice, or 5/2(3/4) = 15/8.

As a result, you need to combine 15 over 4 quarters of sparkling water with 15/8 quarts of grape juice.

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Answer:  250

Step-by-step explanation:

The rate of interest specified in a bond contract as the interest rate to be paid by the company to investors in the bond is known as stated rate, therefore the given statement is false

The given statement is

The rate of interest specified in a bond contract as the interest rate to be paid by the company to investors in the bond is known as market rate

The market price is defined as the price for goods or services is the usual price charged for them in a free market. Therefore the given statement is false and the correct answer is stated price

Hence, The given statement is false because the rate of interest specified in a bond contract as the interest rate to be paid by the company to investors in the bond is known as stated rate

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The 25th percentile is 35 and the 60th percentile is 46.

Given,

The following are the ages of 15 of the signers of the declaration of Independence 47, 46, 54, 31, 50, 46, 27, 62, 40, 39, 50, 44, 35, 30, and 41 Send data to Excel Find 25th and 60th percentiles for these ages.

(a) 25th percentile = (n + 1) * Pth value

                             = (15 + 1) * 0.25th value

                             = 4th value

                             =35

(b) 60th percentile = (n + 1) * Pth value

                               = (15 + 1) * 0.6th value  

                               = 9.6th value

                               =46

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The value of seaweed height that divides the bottom 30%  from the top 70% is 8.96 cm.

What is a Normal distribution in statistics?

Data in a normal distribution are symmetrically distributed and have no skew. The majority of values cluster around a central region, with values decreasing as one moves away from the center. In a normal distribution, the measures of central tendency (mean, mode, and median) are all the same.

Given data:

X: height of seaweed.

       X~N (μ;σ²)

       μ= 10 cm

       σ= 2 cm

We have to find the value of the variable X that separates the bottom 0.30 of the distribution from the top 0.70

              P(X ≤ x) = 0.30

              P(X ≥ x) = 0.70

Now by using the standard normal distribution,

we have to find the value of Z that separates the bottom 0.30 from the top 0.70 and then use the formula

        Z = (X - μ)/σ

translates the Z value to the corresponding X value.

           P(Z ≤ z) = 0.30

In the body of the table look for the probability of 0.30 and reach the margins to form the Z value. The mean of the distribution is "0" so below 50% of the distribution you'll find negative values.

                  z= -0.52

Now you have to clear the value of X:

        Z= (X - μ)/σ

        X= (Z * σ) + μ

       X = (-0.52 * 2) + 10

         = 8.96

hence, the value of seaweed height that divides the bottom 30%  from the top 70% is 8.96 cm.

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The transformations are matched as follows:

All of these transformations are applied to the vertices of the polygons, and each of them have standard definitions, given by formulas, which are matched in this problem.

Hence the rules are matched as follows:

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The equation which represents a linear as required in the task content is; y equals one fourth times x minus 1.

A linear function has one independent variable and one dependent variable in which case the degree of the equation is 1; meaning- the highest power of the variables is 1.

Conventionally, The independent variable in this regard is x and the dependent variable in this regard is y.

The required equation which represents a linear function is; y equals one fourth times x minus 1; y = (1/4)x - 1

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Answer: C

Step-by-step explanation: Took the test

The equation to find the value of w is (4w - 5) + w = 30

and the value of w is 7.

Given, A bag of potatoes and a bag of oranges weigh 30 pounds in all.

The weight of the potatoes is 5 pounds less than 4 times the weight of the oranges.

Let w represent the weight of the oranges

we have to represent an equation to find the value of w.

as the weight of the oranges is w

then, the weight of the potatoes is 4w - 5.

so, the equation be

(4w - 5) + w = 30

5w - 5 = 30

5w = 35

w = 7

Hence, the equation to find the value of w is (4w - 5) + w = 30

and the value of w is 7.

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Answer:

D

Step-by-step explanation:

The cost formula is C(x) = 20x + 18000

Give two instances and an explanation of what a linear equation is ?

A linear equation in two variables is one that has the form ax + by + c=0, where a, b, and c are real integers and the coefficients of x and y, i.e., a and b, respectively, are not equal to zero. The linear equations 10x+4y = 3 and -x+5y = 2 are two-variable examples.

(a) Let a represent the number of canoes produced. The cost C(x) of producing a canoes is then

C(x) = 20x + 18000

(b) If x represents the number of canoes sold, then the revenue R(x) from selling a canoes will be

R(x) = 80x

(c) The break-even point is the x-value where C(x) = R(x) where the revenue generated from selling a canoes matches the cost of producing a canoes. This will happen when

20x + 18000 =80x → 18,000=60x  →  x=300

When 300 canoes are produced, this business will reach break-even threshold.

They will incur a $24,000 expense and generate a $24,000 profit. Anymore than 300 canoes will result in a profit that outweighs the cost. Anything less than 300 canoes will cause their expenses to outpace their income.

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The equation of the circle centered at the origin and passing through the point (-4,0) is [tex]x^2+y^2=16[/tex].

Equation of a circle

A circle may also be defined as a special kind of ellipse in which the two foci are coincident, the eccentricity is 0, and the semi-major and semi-minor axes are equal.

We know that,

Equation of the circle passing through the origin is given by:-

[tex]x^2+y^2=r^2[/tex]

Where,

r is the radius of the circle, and

(x,y) are the coordinates of each point of the circle.

Hence, we can write,

The radius of the circle will be :-

[tex]\sqrt{(0-(-4))^2+(0-0)^2} =\sqrt{ 4^2+0^2} =\sqrt{16}=4 units[/tex]

Hence, r = 4 units.

Hence, the equation of the circle is given by:-

[tex]x^2+y^2=16[/tex]

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Chris earned a total of $192.5 today.

What is the commission rate?

The compensation for a commission is referred to as a commission rate. Some jobs pay a fixed percentage, while others pay a fixed dollar amount depending on the volume of sales.

Given, Chris earns $10 per hour and 12. 5% commission on computer sales.

And, he worked  5.5 hours and sold $1100 in computers

Total earning = 5.5*$10 + $1100*12. 5%

                       = $55 + 1100*(12.5/100)

                       = $55 + $137.5

                       = $192.5

Therefore, Chris earned a total of $192.5 today.

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The 99% confidence interval for the true mean lifespan of the product is, [12.128, 13.872].

What is standard deviation?

The standard deviation in statistics is a measurement of how much a group of values can vary or be dispersed. A low standard deviation suggests that values are often close to the set's mean, whereas a large standard deviation suggests that values are dispersed over a wider range.

Given: A toy maker claims his best product has an average lifespan of exactly 18 years.

A skeptical product evaluator asks for evidence (data) that might be used to evaluate this claim.

The product evaluator was provided data collected from a random sample of 35 people who used the product.

Using the data, an average product lifespan of 13 years and a standard deviation of 2 years was calculated.

As sample size is large we will use z value to calculate confidence Interval 99% confidence Interval is

{x bar} Z_({1 - alpha/2}) (s/√{n})

13\ 2.576* 2/ √13

(12.128, 13.872).

Hence, the 99% confidence interval for the true mean lifespan of the product is, [12.128, 13.872].

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The paragraph is translated from Russian language to English language as "Don't you really think you can learn something for yourself? - Ilya. She spoke with that goal that she hated in herself, i don't believe it. For example, here Vekshina! Exactly,  I don't know"

In translating the paragraph to English, if you're not a native Russian speaker or fully understand the language to read and write, it is advisable to apply an online free tool for this type of exercise. This tool can translate texts as well as words in an image.

Applying that here, the paragraph is roughly best translated as

"Don't you really think you can learn something for yourself? - Ilya. She spoke with that goal that she hated in herself, i don't believe it. For example, here Vekshina! Exactly,  I don't know"

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Its true that the probability of rejecting the null Hypothesis decreases.

What is sample mean?

In mathematics, particularly in statistics, there are various types of means. Each mean summarises a particular set of data, frequently to help determine the overall significance of a particular data set.

The sample mean is a fair estimation of the population mean, according to probability theory. We also observed in our simulations that the means of bigger samples are more likely to be closely grouped around the population mean than the means of smaller samples.

Since, when other things being equal as the sample means get closer to each other.

So, the given statement is true.

Hence, its true that the probability of rejecting the null Hypothesis decreases.

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Answer:

Ratio of men:women is 7:8

Step-by-step explanation:

Total number of people =150

number of women =80

hence number of men = total number of people - total number of women

number of mean =150 -80

= 70

therefore ratio of men: women =70:80

=70/80

=7/8

Answer:

7:8

Step-by-step explanation:

if there are 150 people and 80 are women we just subtract from 150 by 80 to find how many men

150-80

70 men

70: 80 is the ratio from men to women and we treat this like a fraction when simplifying

We divide both sides by 10th get simplest form

7:8

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An absolute value equation to represent the definition of betweenness will be;

⇒ B ∈ A,C ↔  AB +BC = AC

What is Absolute value equation?

An absolute value equation is a function that contains an algebraic expression within absolute value symbols.

Given,

There are three points a, b, and c lie on the same line, then b is between a and c if and only if the distance from a to c is equal to the sum of the distances from a to b and from b to c.

Now,

We need to find the absolute value function for this statement as;

In order to find the absolute value equation,

First we have to identify the symbols for the terms mentioned in the statement as;

Between = ∈

If and only if = ↔

Now, We have to divide the statement as two parts as;

First one is,

"c lie on the same line, then b is between a and c"

It can be written as,

⇒ B ∈ A,C

Then the second part is, "the distance from a to c is equal to the sum of the distances from a to b and from b to c."

Which can be written as

⇒ AB + BC = AC

When we combine it,

Then we get the absolute value equation as,

⇒ B ∈ A,C ↔  AB +BC = AC

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By permutation, in 95040  ways we can choose a starting lineup consisting of a center, a power forward, a shooting forward, a point guard, and a shooting guard

A permutation is a set up of things in a certain sequence. Here, the members of sets or their constituent parts are sorted in a linear or sequential manner.

Take the number of possibilities for each event and multiply it by itself X times, where X is the total number of events in the sequence, to find the number of permutations. For instance, four-character PINs have a total of 10 possible combinations because each digit can vary from 0 to 9.

[tex]12^P_{5} = \frac{12!}{(12-5)!} =\frac{12!}{5!} = 12 X 11 X 10 X 9 X 8 = 95040[/tex]

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