Calculate both outliers​

The constant of proportionality on the equation is 5.

What is constant of proportionality?

Constant of proportionality is defined as the ratio that relates two given value. When two values are directly or indirectly proportional to one another, there relation is expressed as y = kx.

We compare the general direct proportionality relation with the equation given.

The equation given : y = 5x

The direct relationship between y and x is :

y α x

y = kx - - - (1)

Where, y and x are variables and k is the constant of proportionality.

Comparing equation (1) with the equation given :

y = kx

y = 5x

We can observe that, k in the equation (1) equals to 5 in the given equation.

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Ratio in three ways are given below.

The ratio is the number that can be used to represent one quantity as a percentage of another, to put it simply. A ratio's two numbers can only be compared if they share the same unit. Ratios are used to compare two objects. a connection between two values that is typically expressed as the quotient of one value divided by the other. For instance, the ratio of red to blue marbles is 6:4, or six red to four blue marbles, in the case of a box containing six red and four blue marbles. A decimal or percentage can also be used to indicate a ratio.

Given Data

An orchard contains 12 rows of Granny Smith apple trees, 10 rows of Fuji apple trees, 15 rows of Gala apple trees, 2 rows of Golden Delicious apple trees, and 2 rows of Jonathan apple trees.

a) Rows of Gala apple trees to Granny apple smith trees:

Ratio

First way = 15 to 12

Second way = 15:12

Third way = [tex]\frac{15}{12}[/tex]

b) Rows of Fuji apple trees to total number of apple trees

Total number = 12 + 10 + 15 + 2 +2

Total number = 41

Rows of Fuji apple trees = 10

First way = 10 to 41

Second way = 10: 41

Third way = [tex]\frac{10}{41}[/tex]

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The fountain in the city cycles 46.2 gallons of water in every hour if it cycles 69.3 gallons of water every 1.5 hours according to the model equation.

The unitary technique in actuality involves first determining the actual value of a single unit, alongside followed by the value of the necessary number of units.

The unitary approach is a kind of a strategy for problem-solving that involves first determining the value of a single unit, then multiplying that value to determine the required value.

Total mass = 69.3 gallons

Time taken = 1.5 hrs

For 1 hr = 69.3/1.5

= 46.2 gallons

A single or distinct unit is referred to by the word unitary. Therefore, the goal of this strategy is to establish values in reference to a single unit.

The unitary technique, for instance, can be used to calculate how many kilometers a car will go on one liter of gas if it travels 44 km on two liters of fuel.

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The inverse of the function y equals x squared - 10x (y = x² - 10x) is 5 ±√(x + 25).

An inverse function simply refers to a type of function that is obtained by reversing the mathematical operation in a given function (f(x)).

First of all, we would translate the given word sentence into a function as follows:

y equals x squared - 10x  ⇒ y = x² - 10x

In order to determine the inverse of this function f(x) = x² - 10x, we would interchange both the input value (x) and output value (y) as follows:

y = x² - 10x

x = y² - 10y

Next, we would add (half the coefficient of the y-term)² to both sides of the function as follows:

x + (-10/2)² = y² - 10y + (-10/2)²

x + 25  = y² - 10y + 25

x + 25  = (y - 5)²

±√(x + 25)  = y - 5

Adding 5 to both sides of the function, we have:

5 ±√(x + 25) = y - 5 + 5

y = f⁻¹(x) = 5 ±√(x + 25)

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The circumference of circle is [tex]\pi[/tex]d

What is a circle ?

A circle is a two-dimensional object made up of points that are spaced out from a given point (center) on the plane by a fixed or constant distance (radius). The fixed point is referred to as the circle's origin or center, and the fixed distance between each point and the origin is referred to as the radius.

Given that : the circle with area =[tex]\frac{1}{4}\pi d^{2} cm^{2}[/tex]

area of circle is =[tex]\pi r^{2}[/tex]

[tex]\pi r^{2}[/tex]=[tex]\frac{1}{4}\pi d^{2} cm^{2}[/tex]

on comparing we get

r = [tex]\frac{d}{2}[/tex]

circumference of circle is 2[tex]\pi r[/tex]

= 2×[tex]\pi[/tex]×[tex]\frac{d}{2}[/tex]

=[tex]\pi[/tex]d

The circumference of circle is [tex]\pi[/tex]d

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Answer:

8 < L < 30

Step-by-step explanation:

The third side (L) can't be longer than or equal to the sum of the other two.

So. L < 30.

Also, it must be greater than 24-16  ie > 8

0.5 hours

Step-by-step explanation:

60 mph for 7 hours = 60×7= 420 miles

540-420=120 miles left

60mph÷120miles= 0.5 hours

Total deposited = $147600

Interest earned  = $1362693.29

Total no. of years for saving = 65-36-24 = 41

years saving no. of months = 41 x12  

                                              = 492  Month

                                               = $147600

Total deposited = $147600

                     = $1,510,293.29 - $147600

                     = $1362693.29

Interest is a periodically paid interest amount related to the amount borrowed, deposited or borrowed (the so-called capital amount). The total interest on the amount borrowed or borrowed depends on the principal amount, the interest rate, the frequency of the interest and the time of loan, deposit or borrowing.

Annual interest is interest for one year. Other interest rates apply to different periods of time, such as a month or a day, but are usually calculated annually.

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Explanation

the volume of a cone is given by:

Step 1

find the radius:

let

Circumference= 6n inches

radius= r

Step 2

apply the formula for the volume of the cone:

let

h=13 inhces

replace.

so, the answer is

I hope this helps you

The length of the rectangle is 30 feet and the width of the rectangle is 15 feet.

Let l be the length l the rectangle and w be the width of the rectangle.

The area of a rectangular living room is 450 square feet.

⇒ A = l × w

⇒ 450 = l × w                     ................(1)

The length of the room is 15 feet less than three times the width.

So we get an expression,

l = 3w - 15

Substitute above vale of l in equation (1)

450 = (3w - 15) × w        

450 = 3w² - 15w

3w² - 15w - 450 = 0

w² - 5w - 150 = 0

(w - 15)(w + 10) = 0  

w - 15 = 0  or w + 10 = 0

w = 15    or    w = -10

But width of the rectangle cannot be -10

So, w = 15 feet

and l = 3(15) - 15

l = 30 feet

Therefore, the length of the rectangular living room is 30 feet and the width is 15 feet.

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Simplification of the given problems without absolute value sign:

1.  |5-x|-|x+8|, if x>5 is equal to -13.

2.  |x − 2| + |8 − x| + 2, if 2 ≤ x < 8 is equal to 8.

3.  |x − 5| − |2 − x| + |x + 1|, if x ≥ 5 is equal to x -2.

4.  |7 − x| + |4 − 2x| − |x − 8, if x < 2 is equal to 3 -2x.

As given,

Simplification of the given problems without absolute value sign:

1. |5-x|-|x+8|, if x>5

 = x - 5-(x+8)

 = x-5 -x-8

 = -13

2. |x − 2| + |8 − x| + 2, if 2 ≤ x < 8

= x -2+ 8 -x+2

=8

3. |x − 5| − |2 − x| + |x + 1|, if x ≥ 5

 = x-5-(x-2)+(x+1)

=x-5-x+2+x+1

=x-2

4. |7 − x| + |4 − 2x| − |x − 8, if x < 2

= 7-x +4-2x-8 +x

=3-2x

Therefore, simplification of the given problems without absolute value sign:

1.  |5-x|-|x+8|, if x>5 is equal to -13.

2.  |x − 2| + |8 − x| + 2, if 2 ≤ x < 8 is equal to 8.

3.  |x − 5| − |2 − x| + |x + 1|, if x ≥ 5 is equal to x -2.

4.  |7 − x| + |4 − 2x| − |x − 8, if x < 2 is equal to 3 -2x.

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The linear equation of given point (1, -7) and slope -1 is y = -x - 6.

Given:

Point(x₁ , y₁) = (1, -7)

Slope = -1

By using the Point-slope form of the linear equations, we get

y - y₁ = m(x - x₁)

⇒ y - (-7) = -1(x - 1)

⇒ y + 7 = -x + 1

⇒ y = -x + 1 - 7

⇒ y = -x - 6

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27)

Opposite angles are equal.

x° angle is the opposite angle of the 90° angle.

Therefore, x°=90°.

28)

The 90° angle marked in the figure and the y° angles forms a linear pair.

Hence, both angles are supplementary. Supplementary angles sum upto 180°.

Therefore, we can write

Therefore, y°=90°.

29)

In the figure, let z°+46°=p°.

From figure, we can see that the p° angle is the opposite angle of y° angle.

Since opposite angles are equal, we can write

Since from part 28, y°=90°, we get

Therefore, zh=44e.

30)

From figure,

Substitute the known values.

Therefore, w°=224°

Answer:

use keywords together. So I think all you have to do is multiply or add them both together. Try multiplying or adding but I know that those are part of the answer.

Step-by-step explanation:

Line C has the constant of proportionality between y and x of 2/3.

For the given question;

Constant of proportionality = change in y / change in x

Check for each line;

Line A; select any coordinate from the graph.

(7, 3); Put in the formula

Constant of proportionality = 7/3

Thus, Line A has Constant of proportionality between y and x of 7/3.

Line B; select any coordinate from the graph.

(4, 3); Put in the formula

Constant of proportionality = 4/3

Thus, Line B has Constant of proportionality between y and x of 4/3.

Line C; select any coordinate from the graph.

(2, 3); Put in the formula

Constant of proportionality = 2/3

Thus, Line C has Constant of proportionality between y and x of 2/3.

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DOMAIN X CAN BE ALL REAL NUMBERS.

RANGE: Y IS ALL THE REAL NUMBERS GREATER THAN 0.

Step-by-step explanation:

By using the equation to find the slope, we will see that the value of a is -3.

Here we have two points that define a line.

Remember that a linear equation is of the form:

y = m*x + b

Where m is the slope.

And we know that if the line passes through two points (x₁, y₁) and (x₂, y₂), then the slope is:

m = (y₂ -  y₁)/(x₂ - x₁)

In this case, we know that the points are:

(-10, 0) and (a, -6), and the slope is m = -6/7, then we can write the equation:

-6/7 = (-6 - 0)/(a + 10) = -6/(a + 10)

The denominator should be the same in both sides, so we must have:

a + 10 = 7

a = 7 - 10 = -3

Then the two points are (-10, 0) and (-3, -6).

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a. Yes, The situation represents a function.

The independent variable is number of lines and dependent variable is the total cost.

b. The range is 0 ≤ y ≤ 120 and the domain is 0 ≤ x ≤ 4.

What is Domain?

The set of all inputs of the function is called Domain of set.

Given that;

A cell phone plan costs $30 for each line.

Now, Let the number of lines be x and total cost be y.

So, We can evaluate;

y = 30x

Thus, This equation represent Linear function.

So, The situation represents a function.

The independent variable is number of lines and dependent variable is the total cost.

Since, You can have a maximum of four lines on a plan.

So, The possible values are;

x = 0, 1, 2, 3, 4

After substitute all the value of x in equation y = 30x we get;

For x = 0

y = 30 × 0 = 0

For x = 1

y = 30 × 1 = 30

For x = 2

y = 30 × 2 = 60

For x = 3

y = 30 × 3 = 90

For x = 4

y = 30 × 4 = 120

Thus, The range of the function will be 0 ≤ x ≤ 4.

And, The domain of the function will be 0 ≤ y ≤ 120.

Therefore,

a. Yes, The situation represents a function.

The independent variable is number of lines and dependent variable is the total cost.

b. The range is 0 ≤ y ≤ 120 and the domain is 0 ≤ x ≤ 4.

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Answer:

155

Step-by-step explanation:

4(-5)^2-11x

-5 squared is 25, times 4 =100, -11times-5 is 55 (positive) so 100+55=155

243.83

Step-by-step explanation:

Multiple: 38/

3

* 77/

4

= 38 · 77/

3 · 4

= 2926/

12

= 1463 · 2/

6 · 2

= 1463/

6

Answer:

[tex]243 \frac{5}{6}[/tex]

Step-by-step explanation:

Given multiplication:

[tex]12 \frac{2}{3} \times 19 \frac{1}{4}[/tex]

Convert the mixed numbers to improper fractions:

[tex]\implies \dfrac{12 \times 3+2}{3} \times \dfrac{19 \times 4+1}{4}[/tex]

[tex]\implies \dfrac{36+2}{3} \times \dfrac{76+1}{4}[/tex]

[tex]\implies \dfrac{38}{3} \times \dfrac{77}{4}[/tex]

[tex]\textsf{Apply the fraction rule} \quad \dfrac{a}{c}\times\dfrac{b}{d}=\dfrac{ab}{cd}:[/tex]

[tex]\implies \dfrac{38\times77}{3\times4}[/tex]

[tex]\implies \dfrac{2926}{12}[/tex]

Divide the numerator and denominator by 2:

[tex]\implies \dfrac{2926 \div 2}{12 \div 2}[/tex]

[tex]\implies \dfrac{1463}{6}[/tex]

Convert to a mixed number:

[tex]\implies 243 \frac{5}{6}[/tex]

Carmen can determine the length of time she can afford to park her car in the airport parking lot by first deducting the entrance fixed charge from her N dollars and then dividing the balance by the hourly rate.

The standard mathematical operations that combine numbers, variables, and operands to arrive at a defined output value are addition, subtraction, division, and multiplication.

In this situation, we can use the mathematical operations of subtraction and division to determine the length of time Carmen can park her car.

The fixed charge for entering the airport parking lot = $2

Hourly charger after the initial entrance = $3

The total amount of dollars possessed by Carmen = N dollars.

Let the length of time she can park there = l.

The maximum number of hours she can park is given by the function, F(l) = (N - 2)/3.

Thus, the best strategy for Carmen to determine her parking time at the airport parking lot based on her N dollars, the fixed entrance fee, and the variable cost per hour, is using the mathematical operations of subtraction and division.

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Answer:

V= 30m/s u=0 A=1.5, time t=? distance S=?

Step-by-step explanation:

to find time:

A=v-u/t

t=v-u/a

t =30-0/1.5

t = 20 secs

to find distance S

S= UT +½at²

S= 0×20+ 1.5×20²/2

s= 300m

In order to find the solution of this compound inequation, let's first divide it in two inequations:

Solving the first inequation, we have:

Now, for the second inequation, we have:

Putting both solutions together:

So the correct option is C.

If there are three blue marbles, five red marbles, and four green marbles, the probability of selecting a red marble is

Remember that the probability is the ratio between the number of events and the total number of all the events. In this case, the number of events is 5 because there are 5 red marbles, and the total number of all events is the sum of all the marbles.

Therefore, the probability of selecting red marbles is 5/12.

Notice that we have three different ratios, that is because each time we select a red marble it represents a different situation since we won't place back the red marble into the bag, that's why each event decreases by one and each denominator too.

Therefore, the probability of selecting three red marbles without replacement is 15/33.

As we said before, in Part B, we had to multiply each probability for each time we select a red marble. It's important to notice that the numerators decreased by 1 (5,4,3) because each time we select a marble we won't place it back, that's the reason why the denominator also decreased by 1.

The measure of largest exterior angles is 150 degrees

Exterior angles are defined as angles of a polygon formed or created by two the sides of that polygon and sharing a common endpoint.

It is important to note that the exterior angle of a triangle is congruent to the sum of the two non-adjacent interior angles that are opposite to each other.

They are also known to be angles formed by a transversal line as it cuts through one of two lines and it is located on the outside part of the line.

Given the angles as;

Note that the sum of exterior angles are 360degrees

5x° + 9x° + 10x° = 360°

collect like terms

24x = 360

Make 'x' the subject of formula by dividing both sides by 24

x = 360/24

x = 15

But the largest angle is 10x = 10(15) = 150°

Hence, the value is 150°

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average change in price of silver per hour is $ 4  .

With the unitary method, you can solve issues by first calculating the value of a single unit, then multiplying that value by the quantity of units required.

$14 price dropped in 3 and half hours i.e. in 3.5hrs

so in 1 hour price dropped will be = 14 / 3.5

                                                        = $ 4 per hour

therefore average drop rate of price of silver per hour is $ 4  .

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The dollar amount the club would contain if half of the students at the school each provided 50 cents T - 0.5n.

A number, a variable, or a mix of numbers, variables, and operation symbols make up an expression. Two expressions joined by an equal sign form an equation.

The dollar amount the club would contain if they reached half of their goal T + 50.

The dollar amount the club would contain if every student at the school donated 50 cents to the cause 0,5T.

The dollar amount the club could donate if they earned $50 more than their goal of 0.25n.

The dollar amount the club would still require to expand to achieve its goal after every student at the school donated 50 cents 0.5n.

The dollar amount the club would contain if half of the students at the school each provided 50 cents T - 0.5n.

The complete question is:

To support a local senior citizens center, a student club sent a flyer home to the n students in the school. The flyer said, "Please bring in money to support the senior citizens center. Paper money and coins accepted!" Their goal is to raise T dollars. Match each quantity to an expression, an equation, or an inequality that describes it. A: the dollar amount the club would have if they reached half of their goal 1: B: the dollar amount the club would have if every student at the school donated 50 cents to the cause 2: C: the dollar amount the club could donate if they made $50 more than their goal 3: D: the dollar amount the club would still need to raise to reach its goal after every student at the school donated 50 cents 4: E: the dollar amount the club would have if half of the students at the school each gave 50 cents 5: Which statement matches with T + 50?

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Let x be the number of game he can finish in 1 hour

1/4 = 1/3 hour

x = 1 hour

cross-multiply

1/3 x = 1/4

Multiply both-side of the equation by 3

x = 3/4 of his level game

He can finish 3/4 of his level game in an hour