I NEED HELP WITH STATISTICS

Answer:

Let x be the measure of the spacing between the bars.

6.25" + 5x = 36"

5x = 29.75"

x = 5.95"

The three angles equal to x are: ∠x = ∠BAD = ∠BED = ∠BFD

It is proved that, ABHD ||AFED and  proved that AB BD = FD BH

Here, we have,

from the given figure, we get,

CD is a tangent to the circle ABDEF at D.

Chord AB is produced to C.

Chord BE cuts chord AD in H and chord FD in G.

ACFD and AB = EF.

we have,

AC || FD

FE = AB

i) The three angles equal to x are:

∠x = ∠BAD = ∠BED = ∠BFD

as the angles on the same chord.

ii) ∠DBH = ∠DFE [angle on same chord DE ]

∠BDH = ∠FDE [angle inscribed by equal chord]

∠BHD = ∠FED [ when two angles of a triangle are equal so the other will

                               also equal ]

so, we get, by AAA similarity ΔBHD ≡ Δ FDE

iii)  now, we have, from  ΔBHD ≡ Δ FDE

BD/BH = FD/FE

=> BD/BH = FD/AB

=> AB.BD = FD.BH [by cross multiplication]

Hence, Proved.        

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complete question:

CD is a tangent to circle ABDEF at D Chord AB IS produced to C Chord BE cuts chord AD in H and chord FD in G ACI/FD and FE = AB Let ZD4 = and ZD = y 1 2 3 Determine THREE other angles that are equal tox Prove that ABHD ||AFED Hence or otherwise, prove that AB BD = FD BH                      

Pat's approximate monthly Payment would be $304.32 to repay all her loans after the deferment period.

The Pat's monthly payment, we need to consider the terms and interest rates of each loan. Let's break down the calculation step by step:

1. Federally subsidized student loans:

  - Pat receives four annual loans, each for $5400 at an interest rate of 6.5%.

  - Since the loans are annual, we need to calculate the interest for each year and add it to the principal amount.

  - The total principal amount for the four loans is $5400 * 4 = $21,600.

  - The interest for each year is $21,600 * 6.5% = $1,404.

  - Therefore, the total amount owed for the federally subsidized loans is $21,600 + ($1,404 * 4) = $27,816.

2. Private student loan:

  - Pat takes out a private student loan for $4100 at an interest rate of 7.5% for a term of 10 years.

  - The loan is capitalized, which means the interest is added to the principal amount.

  - The total principal amount for the private loan is $4100.

  - The interest for each year is $4100 * 7.5% = $307.50.

  - Since Pat capitalizes the interest for her last year of college, the loan will accrue interest for a total of 9 months.

  - Therefore, the total interest accrued for the private loan is ($307.50 * 9) = $2767.50.

  - The total amount owed for the private loan is $4100 + $2767.50 = $6867.50.

3. Total amount owed:

  - To find the total amount owed by Pat, we add the amounts from the federally subsidized loans and the private loan.

  - Total amount owed = $27,816 + $6867.50 = $34,683.50.

4. Monthly payment:

  - The monthly payment is calculated based on the total amount owed and the repayment term.

  - The term is 10 years for the private loan, but since payments are deferred until 6 months after graduation, the actual term is 10 years - 0.5 years = 9.5 years.

  - The number of monthly payments is 9.5 years * 12 months/year = 114 months.

  - Therefore, the monthly payment is $34,683.50 / 114 months ≈ $304.32.

So, Pat's approximate monthly payment would be $304.32 to repay all her loans after the deferment period.

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Answer:

3/4

Step-by-step explanation:

The 0 <= theta <= pi/2 makes it so the angle must be in the first quadrant. From there, you can use the fact that sin = opposite / hypotenuse.

Thus the opposite side length would be 5, the hypotenuse would be 5, and the adjacent side length would be 3 (by Pythagorean theorem).

Recall that cot = cotangent = 1 / tan. And recall that tan is opposite of adjacent. So tan(theta) = 4/3, and cot (theta) = 3/4.

To find the property tax on the house, we need to calculate the assessed value and then multiply it by the property tax rate.

The property tax rate is $2.45 per $100 of assessed value, which can be written as 0.0245 (since $2.45 divided by $100 is 0.0245).

To calculate the assessed value, we need to find the assessed value as a percentage of the market value. Let's assume the assessed value is x.

x/100 * $250,000 = $a

We don't have the value of 'a,' so we can't directly calculate the assessed value.

Could you please provide the value of 'a' (the assessed value) so that we can calculate the property tax on the house?

~~~Harsha~~~

Answer:

$4,593.75

Step-by-step explanation:

To find the property tax on the house, we need to first determine the assessed value of the house.

If the market value of the house is $250,000, and the assessed value is a dollars, then we can set up the following equation:

a = 0.75 x 250,000

where 0.75 represents the assessment rate, which is typically a percentage of the market value used to determine the assessed value for tax purposes.

Simplifying the equation, we get:

a = 187,500

Therefore, the assessed value of the house is $187,500.

To find the property tax, we can use the given tax rate of $2.45 per $100 of assessed value.

First, we need to convert the assessed value from dollars to hundreds of dollars, which we can do by dividing by 100:

187,500 / 100 = 1,875

Next, we can multiply the assessed value in hundreds of dollars by the tax rate per hundred dollars:

1,875 x 2.45 = 4,593.75

Therefore, the property tax on the house is $4,593.75.

The solution in interval notation is; (-∞,  49/2).

Inequality is defined as the relation which makes a non-equal comparison between two given functions.

To solve the equation 5/16x - 7/4 < 3/4x + 21/2, we can simplify both sides:

5/16x - 7/4 < 3/4x + 21/2

Combining like terms:

5/16x  -3/4x  < 21/2 + 7/4

8/16x < 49/4

1/2x < 49/4

Simplifying the fraction;

x < 49/2

Therefore, the solution in interval notation is (-∞,  49/2).

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The Length of the rod is 3/5 meters.

The civil engineer wants to find the length of a rod that stretches for 1 meter and can be given by the function x=2y^(3/2).

To find the length of the rod, we need to integrate the function x=2y^(3/2) with respect to y. Integrating both sides of the equation,

we have:'int dx = int 2y^(3/2) evaluating the left-hand side gives x = 2/5 y^(5/2) + C, where C is the constant of integration. To find the value of C,

we use the given information that the rod stretches for 1 meter. At y = 0, x = 0 since the rod has no length when it is not stretched. At y = 1, x = 1 since the rod stretches for 1 meter.

Therefore, we have:1 = 2/5 (1)^(5/2) + C1 = 2/5 + CC = 3/5 Substituting C = 3/5 back into the equation for x,

we have:x = 2/5 y^(5/2) + 3/5

The length of the rod is given by the value of x when y = 1. Substituting y = 1,

we have:x = 2/5 (1)^(5/2) + 3/5 = 3/5

The length of the rod is 3/5 meters.

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Answer:

C. 33

Step-by-step explanation:

(√121) (√9) = (√11*11) (√3*3)

                  = (√11^2) (√3^2)

                  = (11)(3)

                   = 33

Answer:

880 feet

Step-by-step explanation:

To find out how many feet a car traveling at 60 miles per hour travels in 10 seconds, we need to convert the speed from miles per hour to feet per second.

1 mile = 5,280 feet (5280 feet = 1 mile)

1 hour = 60 minutes

1 minute = 60 seconds

To convert 60 miles per hour to feet per second, we can use the following steps:

First, convert miles per hour to feet per minute:

60 miles/hour * 5280 feet/mile = 316,800 feet/hour

Then, convert feet per hour to feet per minute:

316,800 feet/hour / 60 minutes/hour = 5,280 feet/minute

Finally, convert feet per minute to feet per second:

5,280 feet/minute / 60 seconds/minute = 88 feet/second

Therefore, a car traveling at 60 miles per hour would travel 88 feet in 1 second. In 10 seconds, it would travel:

88 feet/second * 10 seconds = 880 feet.

[tex]\underset{ \textit{angle in degrees} }{\textit{area of a regular polygon}}\\\\ A=\cfrac{nr^2}{2}\sin(\frac{360}{n}) ~~ \begin{cases} r=\stackrel{ circumcircle's }{radius}\\ n=sides\\[-0.5em] \hrulefill\\ n=10\\ r=13 \end{cases}\implies A=\cfrac{(10)(13)^2}{2}\sin(\frac{360}{10}) \\\\\\ A=845\sin(36^o)\implies A\approx 496.7[/tex]

Answer:

496.7 square units

Step-by-step explanation:

A regular polygon is a polygon with equal side lengths and equal interior angles, meaning all of its sides and angles are congruent.

The radius of a regular polygon is the distance from the center of the polygon to any of its vertices.

The given figure is a regular decagon (10-sided figure) with a radius of 13 units.

To find the area of a regular polygon given its radius, use the following formula:

[tex]\boxed{\begin{minipage}{6cm}\underline{Area of a regular polygon}\\\\$A=nr^2\sin \left(\dfrac{180^{\circ}}{n}\right)\cos\left(\dfrac{180^{\circ}}{n}\right)$\\\\\\where:\\\phantom{ww}$\bullet$ $n$ is the number of sides.\\ \phantom{ww}$\bullet$ $r$ is the radius.\\\end{minipage}}[/tex]

Substitute n = 10 and r = 13 into the formula and solve for A:

[tex]A=10 \cdot 13^2 \cdot \sin\left(\dfrac{180^{\circ}}{10}\right)\cdot \cos\left(\dfrac{180^{\circ}}{10}\right)[/tex]

[tex]A=10 \cdot 169 \cdot \sin\left(18^{\circ}\right) \cdot \cos \left(18^{\circ}\right)[/tex]

[tex]A=496.678538...[/tex]

[tex]A=496.7\; \sf square \; units[/tex]

Therefore, the area of a regular decagon with a radius of 13 units is 496.7 square units (to the nearest tenth).

The nearest tenth, approximately 93.5% of Container A is full after the water is pumped into Container B.

To determine the percentage of Container A that is full after the water is pumped into Container B, we need to compare the volumes of the two containers.

The volume of a cylinder can be calculated using the formula: V = πr^2h, where V is the volume, π is a constant (approximately 3.14159), r is the radius, and h is the height.

For Container A:

Radius (r) = Diameter / 2 = 12 ft / 2 = 6 ft

Height (h) = 14 ft

For Container B:

Radius (r) = Diameter / 2 = 10 ft / 2 = 5 ft

Height (h) = 20 ft

Now, let's calculate the volumes of the two containers:

Volume of Container A = π * (6 ft)^2 * 14 ft ≈ 1,679.65 ft^3

Volume of Container B = π * (5 ft)^2 * 20 ft ≈ 1,570.8 ft^3

To find the percentage of Container A that is full, we need to calculate the ratio of the volume of water in Container B to the volume of Container A:

Ratio = Volume of Container B / Volume of Container A

Ratio = 1,570.8 ft^3 / 1,679.65 ft^3 ≈ 0.9347

Finally, to convert this ratio to a percentage, we multiply it by 100:

Percentage = Ratio * 100

Percentage ≈ 0.9347 * 100 ≈ 93.5%

Therefore, to the nearest tenth, approximately 93.5% of Container A is full after the water is pumped into Container B.

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The required angle is .

Given the triangle and name it as triangle ABC. In triangle ABC, ∠C = 29 and AB =6.78, BC=4, AC = 10.

To find angle A in triangle ABC, use the Law of Cosines, which states:

[tex]c^2 = a^2 + b^2[/tex]- 2ab x cos(C)

That implies,

AB = 6.78 (side a)

BC = 4 (side b)

AC = 10 (side c)

∠C = 29°

Substituting the given values into the Law of Cosines formula, gives:

[tex]10^2 = 6.78^2 + 4^2[/tex] - 2 x 6.78 x 4 x cos(29°)

Simplifying the equation:

100 = 46.2084 + 16 - 54.24 x cos(29°)

Rearranging the equation to isolate the cosine term:

54.24 x cos(29°) = 46.2084 + 16 - 100

54.24 x cos(29°) = -37.7916

Solve for the cosine term:

cos(29°) = -37.7916 / 54.24

cos(29°) = -0.696

To find angle A,  use the inverse cosine (cos⁻¹) function:

∠A = cos⁻¹(-0.696)

Calculating the value of angle A using a calculator or trigonometric table, we find:

∠A = 133.64°

Therefore, angle A in triangle ABC is approximately 133.64°.

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Answer:

D

Step-by-step explanation:

the right triangle contains h , the horizontal leg and the sloping side which is the hypotenuse of the right triangle.

the horizontal leg is half the measure of the side of the square base.

horizontal leg = 8 ÷ 2 = 4

using Pythagoras' identity in the right triangle

the square on the hypotenuse is equal to the sum of the squares on the other 2 sides, that is

h² + 4² = 10² ( subtract 4² from both sides )

h² = 10² - 4² ( take square root of both sides )

h = [tex]\sqrt{10^2-4^2}[/tex]

Answer:

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

Direct variation equation in terms of given values:

10 cm³ of oil has a mass of 9 grams:

Substitute values of m and v and find the value of k:

Substitute the value of k back to initial equation:

The matching choice is B.

Answer:

[tex]m= \frac{9}{10}*v[/tex]

Step-by-step explanation:

Since the mass of cooking oil is directly proportional to the oil's volume, we can write the following equation:

m = kv

where k is the constant of proportionality.

We know that when v = 10, m = 9, so we can plug these values into the equation to solve for k:

9 = k * 10

k =[tex]\frac{9}{10}[/tex]

Now, we can plug k =[tex]\frac{9}{10}[/tex] into the original equation to get the following equation:

m =[tex]\frac{9}{10}[/tex] v

Answer:

8(3+4p)

Step-by-step explanation:

8 goes into 24 and 32, so it can be factored out:

[tex]24+32p=8(3+4p)[/tex]

Answer:

8(3 + 4p)

Step-by-step explanation:

Factor 24 + 32p

First, factor out the GCF. In this case, the GCF is 8, and we have

8(3 + 4p)

We can't factor anymore so the answer is 8(3 + 4p)

Answer: 4

I’m sorry, I could not find any other methods except for finding the closest perfect square which was 2116. (46^2)

Answer:

45

Step-by-step explanation:

The values of b and c is 5 and 6.

To factorize the trinomial x² + 5x + 6, we need to find two integers whose product is 6 and whose sum is 5.

From the given table, we can see that the integers 2 and 3 satisfy these conditions.

Therefore, we can rewrite the trinomial as:

x² + 5x + 6 = x² + 2x + 3x + 6

x² + 2x + 3x + 6 = (x² + 2x) + (3x + 6)

Now, we can factor out the common terms from each group:

x² + 2x + 3x + 6 = x(x + 2) + 3(x + 2)

                          = (x + 2)(x + 3)

Therefore, the factored form of the trinomial x² + 5x + 6 is (x + 2)(x + 3).

Regarding the values of b and c, we can see that b = 5 and c = 6 in the trinomial x² + 5x + 6.

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a.i) The variable cost per haircut is $5.

a.ii) The monthly fixed costs are $2,800

b.i) The break-even point in units is approx. 467 haircuts.

b.ii) The break-even point in dollars is $5,137.

c) The net income, assuming 1,500 haircuts are given in a month, is $6,200.

We shall first break down the costs to estimate the variable cost per haircut and the total monthly fixed costs.

Then, we shall use the results to calculate the break-even point in units and dollars. Lastly, we compute the net income.

a.i) Variable cost per haircut (VC):

Total variable cost per haircut = Commission + Store rent + Barber supplies

Given:

Commission for each haircut per barber = $4

Rent for store per haircut = $0.60

Barber supplies per haircut = $0.40

Price of a haircut (P): $11

VC = $4 + $0.60 + $0.40

= $5

So, the variable cost per haircut is $5.

a.i)Total monthly fixed costs (TFC)

Total monthly fixed costs: Manager's salary + Depreciation on equipment + Utilities + Advertising

Given:

Manager's salary = $1,800

Depreciation on equipment = $500

Utilities =$300

Advertising = $200

TFC = $1,800 + $500 + $300 + $200

= $2,800

Therefore, the total monthly fixed costs are $2,800.

b) Break-even point:

The break-even point is the point: total revenue = total costs.

b.i) Break-even point in units = TFC divided by contribution margin per unit

contribution margin = price - VC

= $11 - $5

= $6

break-even point in units = $2,800 / $6

= 466.67

So, the break-even point in units is ≈ 467 haircuts.

b.ii) Break-even point in dollars:

Break-even point (in dollars) = break-even point (in units) * P

= 467 * $11

= $5,137

Thus, the break-even point in dollars is $5,137.

c) The net income:

Total costs(TC) - Total Revenue (TR):

TR = Number of haircuts * P

= 1,500 * $11

= $16,500

Total Cost (TC) = TVC + TFC

TC = (Variable cost per haircut * Number of haircuts) + Total fixed costs

= ($5 * 1,500) + $2,800

= $7,500 + $2,800

= $10,300

Net income = TR- TC

= $16,500 - $10,300

= $6,200

Hence, the net income, assuming 1,500 haircuts are given in a month, is $6,200.

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Answer:

-1 and -6

Step-by-step explanation:

If you multiply negative times negative or minus times minus it will turn to plus so

- x - = +

-1 x -6 = +6

If you add negative plus negative or minus plus minus it remain negative or minus

- + - = -

-1 + -6 = -7

The two numbers that multiply to 6 and add to -7 are -1 and -6.

We are given two conditions:

xy = 6

x + y = -7

We can rearrange equation 2 to express one variable in terms of the other.

x = -7 - y

Now we can substitute this expression for x in equation 1:

(-7 - y) y = 6

Expanding the equation:

-7y - y²= 6

Rearranging the equation to bring it to a quadratic form:

y² + 7y + 6 = 0

We can now solve this quadratic equation to find the values of y.

Factoring the quadratic equation:

(y + 6)(y + 1) = 0

Setting each factor equal to zero and solving for y:

y + 6 = 0 --> y = -6

y + 1 = 0 --> y = -1

So we have two possible values for y: -6 and -1.

Substituting these values back into equation 2 to find the corresponding values of x:

For y = -6:

x + (-6) = -7

x = -1

For y = -1:

x + (-1) = -7

x = -6

Therefore, the two numbers that multiply to 6 and add to -7 are -1 and -6.

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The measure of angle BDA is 3

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

ABC = 4x - 2

DBC = 3x - 3

The figure is a rhombus

This means that

ABC = 2 * DBC

So, we have

4x - 2 =2 * (3x - 3)

When evaluated, we have

4x - 2 = 6x - 6

When solved for x, we have

2x = 4

So, we have

x = 2

This also means that

BDA = DBC = 3x - 3

So, we have

BDA = 3(2) - 3

Evaluate

BDA = 3

Hence, the measure of angle BDA is 3

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The algorithm justifies the answer of 3/5 as the fraction each person gets.

Representation of the fractions on the second row:

From what you described, two of the loaves were divided into thirds.

This means each person receives one third, and there is one third remaining. Then, this remaining third from the second loaf was further divided into fifths.

Therefore, each person receives one fifth from this remaining third.

So, the representation of the fractions on the second row would be:

Each person receives 1/3 (one third) from the two loaves.

Each person receives 1/5 (one fifth) from the remaining third.

Algorithm/Abstract strategy to justify the 3/5 found as the answer:

To find the final answer of 3/5, we can follow the steps you provided:

Divide two loaves into thirds, giving each person 1/3.

Divide the remaining third from the second loaf into fifths, giving each person 1/5.

Combining the fractions, each person has 1/3 + 1/5.

To add these fractions, we need to find a common denominator. In this case, the least common multiple (LCM) of 3 and 5 is 15. We can convert 1/3 and 1/5 to have a denominator of 15:

1/3 = 5/15 (multiplying numerator and denominator by 5)

1/5 = 3/15 (multiplying numerator and denominator by 3)

Now, we can add the fractions:

5/15 + 3/15 = 8/15

Therefore, each person receives 8/15 of a loaf.

Simplifying this fraction, we get 3/5.

Hence, the algorithm justifies the answer of 3/5 as the fraction each person gets.

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Maria's current age is 15 and Susy's current age is 5.

We have,

Let's denote Maria's current age as M and Susy's current age as S.

We can use the given information to set up a system of equations and solve for their ages.

According to the first statement, "When I have the age that you are, your age will be 2 times that I have," we can write the equation:

M + S = 2(M - S)

Expanding and simplifying:

M + S = 2M - 2S

S + 2S = 2M - M

3S = M

According to the second statement, "When I was 10 years old, you were the age that I am," we can write the equation:

M - 10 = S

Now we have a system of equations:

3S = M

M - 10 = S

To solve the system, we can substitute the value of M from the first equation into the second equation:

3S - 10 = S

Simplifying:

2S = 10

S = 5

Substituting the value of S back into the first equation:

3(5) = M

M = 15

Therefore,

Maria's current age is 15 and Susy's current age is 5.

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The complete question:

Maria tells Susy: "When I have the age that you are, your age will be 2 times that I have and you know that when I was 10 years old, you were the age that I am".

How much do the current ages of both?

Answer:

y = x + 1

Step-by-step explanation:

Parallel lines have same slope.

y = x - 1

Compare with the equation of line in slope y-intercept form: y = mx +b

Here, m is the slope and b is the y-intercept.

m =1

Now, the equation is,

         y = x + b

The required line passes through (-3 ,-2). Substitute in the above equation and find y-intercept,

        -2 = -3 + b

  -2 + 3 = b

         [tex]\boxed{b= 1}[/tex]

    Equation of line in slope-intercept form:

                  [tex]\boxed{\bf y = x + 1}[/tex]      

The equation is :

Solution:

If two lines are parallel to each other, then their slopes are equal. The slope of y = x - 1 is 1. Hence, the slope of the line that is parallel to that line is 1.

We shouldn't forget about a point on the line : (-3, -2).

I plug that into a point-slope which is :

[tex]\sf{y-y_1=m(x-x_1)}[/tex]

Slope is 1 so

[tex]\sf{y-y_1=1(x-x_1)}[/tex]

Simplify

[tex]\sf{y-y_1=x-x_1}[/tex]

Now I plug in the other numbers.

-3 and -2 are x and y, respectively.

[tex]\sf{y-(-2)=x-(-3)}[/tex]

Simplify

[tex]\sf{y+2=x+3}[/tex]

We're almost there, the objective is to have an equation in y = mx + b form.

So now I subtract 2 from each side

[tex]\sf{y=x+1}[/tex]

To determine the balance of iron supplement dose and ordinary food servings needed to meet the patients' nutritional needs, let's assign variables to represent the quantities:

Let:

- x = number of iron supplement doses per day

- y = number of ordinary food servings per day

Based on the information given, we can establish the following equations:

Equation 1: Iron Balance

1.2µg * x + 0.4µg * y = 5.2µg

Equation 2: Potassium Balance

0.3mg * x + 0.1mg * y = 1.3mg

We can solve this system of equations to find the values of x and y that satisfy both equations.

Multiplying Equation 1 by 10 and Equation 2 by 1000 will help us eliminate the decimal points:

Equation 1 (revised): 12µg * x + 4µg * y = 52µg

Equation 2 (revised): 300µg * x + 100µg * y = 1300µg

Now, we can use any method to solve the equations. Let's solve them using the substitution method:

From Equation 1 (revised), we can express x in terms of y:

12µg * x = 52µg - 4µg * y

x = (52µg - 4µg * y) / 12µg

x = (13µg - µg * y) / 3µg

x = 13/3 - y/3

Substituting this value of x into Equation 2 (revised):

300µg * (13/3 - y/3) + 100µg * y = 1300µg

Simplifying and solving for y:

(3900µg - 100µg * y + 100µg * y) / 3 = 1300µg

3900µg / 3 = 1300µg

1300µg = 1300µg

The equation is satisfied for any value of y. This means that there is no unique solution for the system of equations. In other words, any combination of iron supplement doses (x) and ordinary food servings (y) that satisfy the equation 1.2µg * x + 0.4µg * y = 5.2µg will also satisfy the equation 0.3mg * x + 0.1mg * y = 1.3mg.

Therefore, there are multiple ways to achieve the balance of iron and potassium needed to meet the patients' nutritional needs. The specific values of x and y will depend on the preferences of the patients and the dosing recommendations by healthcare professionals.

Answer:

12

Step-by-step explanation:

Answer:

To write the result in lowest terms, we need to simplify the fractions by dividing both the numerator and the denominator by their greatest common factor (GCF). Here are the solutions for each problem:

1.) -15-(5)= -20. This is already in lowest terms because it is an integer.

2.) 5/9 divided by 10/18= (5/9) * (18/10) = 90/90 = 1. This is in lowest terms because the GCF of 90 and 90 is 90.

3.) 2/5+4/7= (14/35)+(20/35) = 34/35. This is in lowest terms because the GCF of 34 and 35 is 1.

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Answer:

B) Subtract 6 from both sides of the inequality.

Step-by-step explanation:

By doing so, we have the following:

x/2 + 6 > 42

x/2 + 6 > 42 - 6

x/2 > 36

(x/2)*2 > 36*2

x > 72

Answer:

B. subtract 6 from both sides of the inequality.

Step-by-step explanation:

Kendall, when solving inequality, would isolate the variable, x.

The first step will be to subtract 6 from both sides of the inequality:

[tex]\frac{x}{2} + 6 > 42\\\frac{x}{2} + 6 (-6) > 42 (-6)\\\frac{x}{2} > 36[/tex]

The next step will be to multiply 2 to both sides of the inequality:

[tex]\frac{x}{2} > 36\\\frac{x}{2} *2 > 36 *2\\x > 36 * 2\\x > 72[/tex]

x > 72 would be the answer.

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Answer:

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The Constant of proportionality (r) in the equation x = ry is 1/11.

The constant of proportionality (r) in the equation x = ry, where x and y are proportional, we can use the given pairs of values for x and y and solve for r.

Let's consider the given pairs of values:

x = 3, y = 33

x = 30, y = 3030

x = 10, y = 1010

x = 100, y = 100100

x = 16, y = 1616

x = 160, y = 160160

We can select any pair of values and set up the equation x = ry. Let's choose the pair x = 3 and y = 33:

3 = r * 33

To find r, we divide both sides of the equation by 33:

r = 3 / 33 = 1 / 11

Therefore, the constant of proportionality (r) in the equation x = ry is 1/11.

We can verify this by substituting other pairs of values into the equation and checking if the equation holds true. For example, let's substitute x = 160 and y = 160160:

160 = (1/11) * 160160

160 = 14560

The equation holds true, confirming that the constant of proportionality is indeed 1/11.

Hence, the constant of proportionality (r) in the equation x = ry is 1/11.

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