Find the equation of the line joining the points (2,-8) and (5,6)

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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The biggest mortgage loan Jenny can afford will be determined using the Excel formula PV(.035/12, 15*12, -485) in the situation that has been provided.

A formula in Microsoft Excel is an expression that modifies values in a set of cells.

Even if the result is incorrect, these formulas nonetheless return a result.

We may execute calculations like addition, subtraction, multiplication, and division using Excel formulae.

To make complex computations simpler, Excel features prewritten formulas known as functions.

A function takes one or more values, runs an operation, and then outputs the outcome to a cell.

Arguments are the values that you pass to a function.

So, in the given situation of Jenny, the excel formula PV(.035/12, 15*12, -485)will be used to determine the largest mortgage loan she can afford.

Therefore, the biggest mortgage loan Jenny can afford will be determined using the Excel formula PV(.035/12, 15*12, -485) in the situation that has been provided.

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Complete question":
Jenny has decided that she can afford a monthly mortgage payment of $390. She has been offered a 3.5% 20-year mortgage from her bank. What formula could you type into Excel to determine the largest mortgage loan she can afford is?

(A) PV(.035/12, 15*12, -485)

(B) PMT(.035/12, 15*12, -485)

(C) PV(.035, 15*12, -485)

(D) 390*.035/20

The area of the shaded region will be equal to 120 square cm.

The space occupied by any two-dimensional figure in a plane is called the area. The space occupied by the rectangle in a two-dimensional plane is called the area of the rectangle.

Given that the sides of the rectangle are 24 cm and 10 cm. The area of the shaded region will be calculated by subtracting the area of the whole rectangle and the area of the triangle which is not shaded.

Area of the shaded region = ( 24 x 10 ) - ( 1/2 x 24 x 10)

Area of the shaded region = 240 - 120

Area of the shaded region = 120 square cm

Therefore, the area of the shaded region will be equal to 120 square cm.

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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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Answer:sales tax rate would be 0.1

using the formula

Sales tax rate = Sales tax percent / 100

Answer:

-5

Step-by-step explanation:

The rate of change, also known as slope, would be -5.

Slope can be found with two points and the formula y minus y divided by x minus x or the change of y divided by the change in x.

To identify the slope on the equation is easy since this is slope-intercept form.

y=mx+b

where m is the slope

m in this case is -5, so -5 is your answer

The distance is 244.56 feet, in feet, between point K and point L.

If ABC is a triangle with AC as the hypotenuse and angle B with 90 degrees then we have:

|AC|^2 = |AB|^2 + |BC|^2    

where |AB| = length of line segment AB. (AB and BC are rest of the two sides of that triangle ABC, AC being the hypotenuse).

Recall the Pythagorean theorem formula:

a² + b² = c²

Given that Kim is standing on the deck, point k, which is 140.75 feet above ground level.

Louise point L, is standing 200ft from the base of the lighthouse directly below Kim’s position.

Thus the distance, in feet, between point K and point L

Replacing by the values we have;

200 ² + 140.75² = KL²

KL² = 59810.56

KL = 244.56

The distance is 244.56 feet, in feet, between point K and point L.

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The speed is 181.5 feet per second. Then the parachutist fall during 15 seconds of free fall will be 2,722.5 feet.

Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.

A parachutist's rate during a fast drop arrives at 55 meters each second. In your calculations, accept that the meter is equivalent to 3.3 feet.

Convert the speed into feet per second. Then we have

S = 55 x 3.3

S = 181.5 feet per second

The parachutist fall during 15 seconds of free fall will be given as,

D = 181.5 x 15

D = 2,722.5 feet

The speed is 181.5 feet per second. Then the parachutist fall during 15 seconds of free fall will be 2,722.5 feet.

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Answer:

4:81

Step-by-step explanation:

κμΛζΖυ

The ratio of area of squares is 4:81. Therefore, option C is the correct answer.

The ratio is defined as the comparison of two quantities of the same units that indicates how much of one quantity is present in the other quantity.

Given that, the ratio of perimeters of a squares is 2:9.

We know that, perimeter of square is 4a, where a is side of a square

Now, 4x/4y =2/9

x/y =2/9

As we know area of square is a², where a is side of a square

So, x²/y² =2²/9²

x²/y² =4/81

The ratio of area of squares is 4:81. Therefore, option C is the correct answer.

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"Your question is incomplete, probably the complete question/missing part is:"

If the ratio of perimeters of a squares is 2:9, then the ratio of their areas is

A) 2:9

B) 5:21

C) 4:81

D) 8:729

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.

[tex]VT=SR \implies 3y+7=25 \implies \boxed{y=6} \\ \\ \\ ○\ m\angle UTV=180^{\circ}-90^{\circ}-29^{\circ}=61^{\circ} \\ \\ \angle WRS \cong \angle UTV \implies 8x-27=61 \implies \boxed{x=11}[/tex]

The reading time calculated to be

The problem involves multiplication of fractions

The fraction required are:

let the reading time be x

1/2 time for 1 hour = 1/2 * x = x/2

three times a week

= x/2 * 3

= 3x/2

The reading time is 3/2 improper fraction and 1 1/2 mixed fraction

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Answer:

It will take 64 hours

Step-by-step explanation:

It will be more specifically 63.889 hours, but rounding up it's 64

A corporation—also known as a C corp—is a legal entity distinct from its owners.

A corporation also referred to as a C corp, is a separate legal entity from its owners.

Corporations are able to generate revenue, pay taxes, and face legal consequences.

The strongest protection against personal liability is provided to owners by corporations, although forming a corporation is more expensive than creating other types of entities.

A corporation is a collection of people or a business that has been given legal status as a single entity by the state and is used for specific legal purposes.

Early corporations were created with a charter.

The majority of governments currently permit the registration of new corporations.

Therefore, a corporation—also known as a C corp—is a legal entity distinct from its owners.

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Correct question:
Which form of organization is a separate legal entity?

The possible ways the corner convenience store can sell candy packages to spend at least $3.00 is

An equation is a mathematical model showing the equality of two opposite sides or an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.

The given parameters are

20c, 30c and 50c

Least cost =$3

Let the possible ways be x

20x+30x+50x=3.00

Solving the equation we have:

100x=3.00

make x the subject

100x=3

x=3/100

This can be expressed in decimal as 0.03

In conclusion, he can sell it in 3/100 or 0.03 ways to spend at least $3.00 on a candy.

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When the costs of the two plans are equal, plan A will cost $37.81, whereas plan B will cost $25.65.

To find the number of calls at which the two plans cost the same, we need to set the costs equal to each other and solve for the number of minutes. The cost of plan A is $19 + $0.11 per minute, and the cost of plan B is $0.15 per minute. Setting these equal to each other, we get:

$19 + $0.11 per minute = $0.15 per minute

We can then solve for the number of minutes by dividing both sides by the per-minute cost:

$19 / $0.11 per minute = $0.15 per minute / $0.11 per minute

This simplifies to:

171 minutes = 135 minutes

Therefore, the two plans cost the same at 171 minutes of calling.

To find the cost at this point, we can substitute 171 minutes back into either of the original cost equations:

Plan A: $19 + $0.11 per minute × 171 minutes = $19 + $18.81 = $37.81

Plan B: $0.15 per minute × 171 minutes = $25.65

Thus, the cost when the two plans cost the same is $37.81 for plan A and $25.65 for plan B.

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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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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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7) ∠EFG = 88 degree

8) DC and AB are parallel to each other.

AE and AB are perpendicular to each other

CG and AB are perpendicular to each other.

9) ∠ACD = 102 degree

What do you mean by co interior angle?

Co-interior angles, or consecutive interior angles, are two angles on the same side of a transverse line. Co interior angles are interior angles that add up to 180 degrees. This means that the sum of the two interior angles on the same side of the horizontal side are complementary.

7) Given :

∠EFG = 32 degree

∠GFH = 56 degree

∠EFG = ∠EFG + ∠GFH = 32 + 56 = 88 degree

Therefore, ∠EFG = 88 degree

8) DC and AB are parallel to each other.

AE and AB are perpendicular to each other

CG and AB are perpendicular to each other.

9) As AB and CD are parallel to each other therefore , ∠BAC and ∠ACD are cointerior angle and sum of co interior angles is 180 degree.

6x + 6 + 9x - 6 = 180

15x = 180

x = 180/15 = 12

∠ACD = (9x - 6) degree = 9(12) - 6 = 108 - 6 = 102

Therefore, ∠ACD = 102 degree

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Answer:

slope of line q = [tex]\frac{3}{4}[/tex]

Step-by-step explanation:

calculate the slope of line p using the slope formula

m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]

with (x₁, y₁ ) = (8, 7 ) and (x₂, y₂ ) = (4, 4 )

m = [tex]\frac{4-7}{4-8}[/tex] = [tex]\frac{-3}{-4}[/tex] = [tex]\frac{3}{4}[/tex]

• Parallel lines have equal slopes

then slope of line q = [tex]\frac{3}{4}[/tex]

Answer: The expression a²+4b² can be factored in the following way:

a²+4b² = (a² + 2ab + 2ab + 4b²)

= (a+b)²

In general, the square of a binomial (a+b) can be written as (a+b)² = a² + 2ab + b². This is known as the "square of a sum" formula. In this case, we can apply this formula to the binomial a+b to obtain a² + 2ab + b² = (a+b)². We can then use the fact that the square of a binomial can be written as the square of each term plus twice the product of the two terms. This allows us to write the expression as (a+b)² = a² + 2ab + b² = a² + 2ab + 2ab + 4b² = (a² + 2ab + 2ab + 4b²) = (a²+4b²). Therefore, the fully factored form of a²+4b² is (a+b)².

Answer:

-2

Step-by-step explanation:

If both sides are identical, there will be infinitely many solutions.

The critical value that corresponds to a confidence level of 99% is, 2.58.

1 decimal place (tenths) 2 decimal places (hundredths) 3 decimal places (thousandths) 4 decimal places (ten-thousandths)

The confidence level is 99%.

The significance level is:

Compute the critical value as follows:

That is:

Use the z-table for the z-value.

For z = 2.58 the P (Z < z) = 0.995.

And for z = -2.58 the P (Z > z) = 0.005.

Thus, the critical value is, 2.58.

active attachment

"=NORM.INV(0.0635,0,1)"

"=NORM.INV(1-0.0635,0,1)"

Previous concepts

And we can use the following excel codes to find the solution:

"=NORM.INV(0.0635,0,1)"

"=NORM.INV(1-0.0635,0,1)"

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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 probability that a resident own a cat or a dog is 48%

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

P(Own a cat) = 70%

P(Own a dog) = 59%

P(Own a cat and a dog) = 42%

The probability a resident own a cat or a dog is then calculated as

Probability a resident own a cat or a dog = P(Own a cat) + P(Own a dog) - P(Own a cat and a dog)  

Substitute the known values in the above equation, so, we have the following representation

Probability a resident own a cat or a dog = 70% + 59% - 42%

Evaluate the sum and the difference

Probability a resident own a cat or a dog = 48%

Hence, the probability is 48%

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Complete question

59% of all the town's residents own a dog and 70% own a cat. Of the dog owners 42% also own a cat. If a town resident is chosen at random find:

the probability a resident own a cat or a dog

(round to 4 decimal places where possible)

We know that we need to sell out 53 candles to break even using mathematical operations.

The process of calculating a value using operands and a math operator is known as a mathematical "operation."

The provided operands or integers must follow certain established rules that are associated with the math operator's symbol.

PEMDAS stands for Parentheses, Exponents, Multiplication, Division, and Addition Subtraction (from left to right).

So, the total expense of the shop:

$100 + $32.50 = $132.50

No, the candle costs $2.50.

The selling price of a candle is $5.

Profit in each candle is: 5 - 2.50 = $2.50

A number of candles that we need to sell to break even are:

132.50/2.50

53

Therefore, we know that we need to sell out 53 candles to break even using mathematical operations.

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The possible number of 3 -letter words that can be formed with given conditions.

(a) No condition is imposed: 343

(b) No letter can be repeated in a word: 210

(c) Each word must begin with the letter 'a' : 49  

(d) The letter 'c' must be at the end: 49

(e) The second letter must be a vowel: 98

In this question we have been given that 3 -letter words' are formed using the letters a, b, c, d, e, f, g.

We need to find the possible number of 3 -letter words that can be formed with given conditions.

(a) No condition is imposed.

the possible number of 3 letters words would be,

7³ = 343

(b) No letter can be repeated in a word.

Using the formula of Permutation,

^{7}P_3 = 7!/(7 - 3)!

             = 210    

(c) Each word must begin with the letter a.  

If each word begins with letter 'a' there would be possible combinations of remaining 6 letters at 2nd and 3rd position of 3-letter word.

So, the possible number of 3 letters words would be,

7² = 49  

(d) The letter c must be at the end.

If each word ends with letter c there would be possible combinations of remaining 6 letters at 1st and 2nd position of 3-letter word.

So, the possible number of 3 letters words would be,

7² = 49  

(e) The second letter must be a vowel.

In the 3 letter word, the second letter must be vowel which is either a or e.

So, the possible number of 3 letters words would be,

49 + 49 = 98

Therefore, the possible number of words would be (a) No condition is imposed: 343

(b) No letter can be repeated in a word: 210

(c) Each word must begin with the letter 'a' : 49  

(d) The letter 'c' must be at the end: 49

(e) The second letter must be a vowel: 98

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The complete question is:

3 -letter words'' are formed using the letters a, b, c, d, e, f, g. How many such words are possible for each of the following conditions?

(a) No condition is imposed.

(b) No letter can be repeated in a word.

(c) Each word must begin with the letter a.

(d) The letter c must be at the end.

(e) The second letter must be a vowel.