A new park was designed to contain two circular gardens. Garden A has a diameter of 65 m, and B has a diameter of 85 m.


A. If the gardener wants to outline the gardens in edging, how many meters will be needed to outline

the smaller garden? (Write in terms of P.I.E.)


B. How much more edging will be needed for the larger garden than the smaller one?


C. The gardener wishes to put down weed block fabric on the two gardens before the plants are

planted in the ground. How much fabric will be needed to cover the area of both gardens?

Given the equivalent ratios:

4:12 and 11:x

To get an equivalent ratio, the denominator and numerator of one ratio is multiplied or divided by the same non zero number.

To find the value of x, we have:

The value of x = 33

ANSWER:

33

The probability is the ratio of the favorable event to the total number of events. Then the probability is 0.76%.

Probability means possibility. It deals with the occurrence of a random event. The value of probability can only be from 0 to 1. Its basic meaning is something is likely to happen.

The Art Club is displaying the students' works in the main hallway. In a row of 12 randomly ordered paintings.

Then the probability that Tim's and Abby's paintings are in the 6th and 7th positions will be

\(P = \dfrac{1}{^{12}P_2} \\\\\\P = \dfrac{1}{\dfrac{12!}{(12-2)!}}\\\\\\P = \dfrac{1}{132}\\\\\\P= 0.007575 \approx 0.0076 \ or \ 0.76 \%\)

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Answer:

-4/2x+3 or if you simplyfy it will be -2x+3

Step-by-step explanation:

Answer:

\(y = -\frac{1}{2}x + 3\)

-3a-4a×2+10+4×9a+1-5b×6

-3a-8a+10+36a+1-30b

-11a+36a-30b+10

25a-30b+10

5(5a-6b+2)

Answer:

23x+42x

=65x

Hope it helps

The equivalent exponential decay function is given as \(m(t)=18000(0.81)^t\)

An exponential function is in the form

y = abˣ

where y, x are variables, a is the initial value of y and b is the multiplier.

Let m(t) represent the value of the car after t years, hence the exponential decay is given by:

\(m(t) = 18000(0.9)^{2t}\\\\m(t)= 18000(0.9)^{2(t)}\\\\m(t)=18000(0.81)^t\)

The equivalent exponential decay function is given as \(m(t)=18000(0.81)^t\)

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Answer: $29.00

Step-by-step explanation: $14.50×2

Answer:

3x = 3

Step-by-step explanation:

Since for 3x = 3, we can plug in the 1.

It becomes:

3(1) = 3

3 = 3

Thus, 3x =3 would be true if x = 1.

Answer:

f (3) equals -11

Step-by-step explanation:

f (x) = -4x + 1

For f(3), just substitute 3 in the place of x:-

f (3) = -4 x 3 + 1

f (3) = -12 + 1

Answer:

-11

Step-by-step explanation:

where x is out -3 so it would look like

-4(3)+1

which is -11

you do -4 * 3 first which = -12 than add one you will get -11

Answer:

y=-6x+36

Step-by-step explanation:

у + 6x — 36 = 0

-add 36 to both sides

y+6x=36

-subtract 6x from both sides

y=36-6x or y=-6x+36

-This should be the correct answer

Answer:

each side has to be the same for the triangle to be congruent

Answer:

In this case SAA is a valid means for establishing triangle congruence. You can see in the following image. The triangles are the same, SAA is a valid means for establishing triangle congruence. You can see in the following image. The triangles are the same, in other words congruent. How I figured it out was by making a random triangle (ABC) then finding the lengths and angles.  From there, I picked a random side (AB) and angles (A) and (B) after I transferred the information I had and put it into a new triangle. Using this formula to determine the third angle: 3rd angle (C = 45*) = 180* - angle A (45*) - angle B (90*). From there, I looked for where line (BC) and (CA) would connect. Leaving me with two congruent triangles.

(ﾉ◕ヮ◕)ﾉ*:･ﾟ✧

a. The market equilibrium price can be found by setting the quantity demanded equal to the quantity supplied. In this case, we have Pd = Ps, so we can set -10Qd + 80 = 2Qs + 20. Solving for Qs, we get Qs = (60 + 10Qd)/2.

b. To find the market equilibrium quantity, we substitute the value of Qs into the equation for Ps: Ps = 2Qs + 20. Plugging in the value of Qs, we get Ps = (60 + 10Qd)/2 + 20. Simplifying this equation, we find Ps = (30 + 5Qd) + 20, which simplifies further to Ps = 50 + 5Qd.

c. Consumer surplus represents the difference between the price consumers are willing to pay and the market equilibrium price. To calculate the consumer surplus, we need to find the area of the triangle above the market equilibrium quantity and below the demand curve. In this case, the demand curve equation is Pd = -10Qd + 80.

d. Producer surplus represents the difference between the market equilibrium price and the price producers are willing to sell at. To calculate the producer surplus, we need to find the area of the triangle below the market equilibrium quantity and above the supply curve. In this case, the supply curve equation is Ps = 2Qs + 20.

e. Total surplus is the sum of the consumer surplus and the producer surplus.

f. To graph the market, we can plot the demand and supply curves on a graph with price on the y-axis and quantity on the x-axis. We can label the equilibrium price and quantity as the point where the demand and supply curves intersect. The consumer surplus and producer surplus can be represented by shaded areas on the graph.

The specific values for the market equilibrium price, quantity, consumer surplus, producer surplus, and total surplus cannot be determined without additional information or values for Qd.

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Answer:

x=-6/11, y=-61/11. (-6/11, -61/11).

Step-by-step explanation:

4x+7y=-41

x=y+5

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

4(y+5)+7y=-41

4y+20+7y=-41

11y=-41-20

11y=-61

y=-61/11

x=-61/11+5=-61/11+55/11=-6/11

Answer: The probability is 50%.

Step-by-step explanation: The probability that both are girls if the older child is a girl can be calculated through probability. First, we know that there are two genders the child can be, male or female. When we have 2 possible outcomes, the probability of each outcome is 50%. We know the first child is a girl, and that the second child has a 50% chance of being a girl, so the probability is 50%.

Thad would be 4 5/12 feet next year

Fractions are defined as the part of a whole number, a whole variable or a whole element.

In mathematics, there are different fractions,

These fractions are listed as;

From the information given, we have that;

Thad is  4 1/6 feet tall.

Next year he add 1/4 foot

Convert to improper fraction

25/6 + 1/4

Find the LCM, we have;

50 + 3/12

53/12

4 5/12 feet

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Answer: \(\dfrac{200}{S}\) represents the transport cost per student in the expression.

Step-by-step explanation:

Given: For trip,

Admission fee per student = $10

Transport cost (for all students0 = $200

Here, S represents the number of students  went on the field trip.

Transport cost per student = (Total cost) ÷ Total student

So, \(\dfrac{200}{S}\) represents the transport cost per student.

Hence,  \(\dfrac{200}{S}\) represents the transport cost per student in the expression.

Answer:

0.25 = one time charge

Step-by-step explanation:

Given that:

Charging pattern of store for scanning documents :

(One time fee + fixed amount per page scanned)

The equation:

y=0.10x+0.25 ; gives the total cost of scanning x document pages

Comparing the equation and the charging pattern :

y = total cost

0.10 = fixed cost per page

x = number of pages scanned

0.25 = one time charge(not dependent on number of pages to be scanned).

Answer:

$391.2 per owner

Step-by-step explanation:

find the total price of the items and divide it by five

Answer:

12

Step-by-step explanation:

12 is the area

Since,

6×2=12

The five values for a data set are: minimum = 0 lower quartile = 2 median = 3. 5 upper quartile = 5 maximum = 10 Bruno created the box plot using the five values. Bruno made error. The left whisker should go from 0 to 2.

Quartiles is a type of quartile that divides data into four parts with approximately the same number. The first quartile or lower quartile (Q1) is the middle value between the smallest value and the median of the data group. The first quartile is a marker that the data in that quartile is 25% below the data group.

The second quartile (Q2) is the median data which marks 50% of the data (dividing the data in half). The third or upper quartile (Q3) is the middle value between the median and the highest value of the data set. The third quartile is a marker that the data in that quartile is 75% below the data group. Quartiles are a form of an ordered statistic because to determine quartiles, data needs to be sorted from smallest to largest value first.

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Answer:

c and d

Step-by-step explanation:

c) Housing, savings and food = 54%

d) Housing, food and transportation = 60%

Answer:

c and d

Step-by-step explanation:

The given system of equations do not have a solution since their related line equations have the same slope.

The given system of equations is:

-x + 5y = 3   .......... (1)

2x - 10y = 4   ........(2)

In Equation (1), add both sides by (-5y)

-x + 5y + (-5y) = 3 + (-5y)

-x = -3 - 5y

Multiply by (-1)

x = 3 + 5y

Substitute x = 3 + 5y into equation (2)

2x - 10y = 4

2.(3 + 5y) - 10y = 4

6 + 10y - 10y = 4

6 = 4 (False)

Since the last equation is false, we might suspect that the given system of solution does not have solutions.

We need to check the slope of both equations:

-x + 5y = 3

⇒ 5y = x + 3

⇒ y = 1/5 x + 3/5

2x - 10y = 4

⇒ -10 y = -2x + 4

⇒ y = (2/10) x - 4/10

⇒ y = 1/5 x - 2/5

We can see that both equations have the same slope, i.e. 1/5.

Hence, they do not have solutions since the lines are parallel to each other.

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Answer:

pi/6, 5pi/6, 7pi/6, 11pi/6

Step-by-step explanation:

3(sec x)^2 -4=0

Add 4 on both sides:

3(sec x)^2=4

Divide 3 on both sides:

(sec x)^2=4/3

Take square root of both sides:

sec x=plus/minus sqrt(4/3)

Reciprocal identity:

cos x=plus/minus sqrt(3/4)

Simplify the radical:

cos x=plus/minus sqrt(3)/2

So we are looking on the unit circle where the first coordinate of the order pair is either sqrt(3)/2 or -sqrt(3)/2.

This happens at pi/6, 5pi/6, 7pi/6, 11pi/6

Answer:

\(\sf \boxed{\sf x = \dfrac{\pi}{6},\dfrac{5\pi}{6},\dfrac{7\pi}{6},\dfrac{11\pi}{6}}\)

Step-by-step explanation:

A trigonometric equation is given to us , and we need to find the solutions of the equation within the interval [ 0,2π ]

The given equation is ,

\(\sf\longrightarrow 3(sec x)^2-4=0 \)

This can be written as ,

\(\sf\longrightarrow 3sec^2x - 4 = 0 \)

Add 4 to both sides of the equation ,

\(\sf\longrightarrow 3sec^2x = 4 \)

Divide both sides by 3 ,

\(\sf\longrightarrow sec^2x =\dfrac{4}{3} \)

Put squareroot on both sides ,

\(\sf\longrightarrow sec \ x =\sqrt{\dfrac{4}{3} }\)

Simplify ,

\(\sf\longrightarrow sec\ x =\pm \dfrac{2}{\sqrt3} \)

Multiply numerator and denominator by √3 ,

\(\sf\longrightarrow \bf sec(x) = \dfrac{ 2\sqrt3}{3},-\dfrac{2\sqrt3}{3} \)

Solve for x ,

\(\sf\longrightarrow x = \dfrac{\pi}{6} +2\pi n , \dfrac{11\pi}{6}+2\pi n , \textsf{ for any integer n } . \)

Therefore all the possible solutions are ,

\(\sf\longrightarrow \boxed{\blue{\sf x = \dfrac{\pi}{6},\dfrac{5\pi}{6},\dfrac{7\pi}{6},\dfrac{11\pi}{6}}} \)

Answer:

Step-by-step explanation:

The radius is 6 inches uw :)

Answer:

An arc of a circumference or of a circle mostly is a portion of the circumference. The length of an arc for all intents and purposes is simply the length of this portion of the circumference in a definitely major way. The circumference itself can particularly be considered an arc that goes around the circle in a fairly major way.

Answer:

x = 12

Step-by-step explanation:

If 'a number' is x,

3x = 36

x = 36/3 = 12

Example of the range of a function is given as follow:

f(x) = 2x + 1 , x∈N, x < 5 then its range is equal to { 3, 5, 7, 9}.

As given in the question,

Range of any given function is defined as collection of all the output values of the given function.

Let us consider an example to represent the range of the given function:

f(x) = 2x + 1 where x ∈ N , x < 5

Here x belongs to natural numbers less than 5 which implies x is equal to 1, 2, 3, 4.

Substitute the values of x to get the range (output values ).

f(1) = 2(1) + 1

    = 3

f(2) = 2(2) + 1

     = 5

f(3) = 2(3) + 1

     = 7

f(4) = 2(4) + 1

     = 9

Range of f(x) = { 3, 5, 7, 9 }.

Therefore, the range of any function is its output values example

f(x) = 2x + 1 , x ∈ N , x < 5 have range = { 3,5,7,9}.

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Answer:

0.13 cm per second

Step-by-step explanation:

Lets convert the minutes to seconds:

3/4 minutes = 3/4(60) = 45 seconds

The snail traveled 5.85 cm in 45 seconds

To find out the speed per second, we set up a proportion:

\(\frac{5.85}{45} = \frac{x}{1}\)      where 45 and 1 represent the number of seconds, and 5.85 and x represent the distance in that set of time

Let's solve for x, or the distance in 1 second:

\(\frac{5.85}{45}=\frac{x}{1}\\\\\\\frac{5.85*1}{45x}\\\\\\x = \frac{5.85}{45}\\\\\\\\\\x = 0.13\)

The snail travels 0.13 cm per second.

-Chetan K

Answer: x= -16

Step-by-step explanation:

The solution to the system in given tables of line 1 and line 2, using linear equation is (b) (0,5)

A linear equation is one that has a degree of 1 as its maximum value. No variable in a linear equation, thus, has an exponent greater than 1. A linear equation's graph will always be a straight line.

from the table of line 1, the equation of line is

y = 2x +5.

from the table of line 2, the equation of line is

y = 5 - x

to find the solution of the system, we compare both of the equation, we get

2x + 5 = 5 - x

add x from both side, we get

3x + 5 = 5

subtract 5 from both side, we get

3x = 0

So that, x = 0

putting the value of x in the equation of line 2

y = 5 - x

y = 5 - 0

y = 5

The solution to the system in given tables of line 1 and line 2 is (0,5)

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We can also plot the vertical asymptote at x = -1/3 and the horizontal asymptote at y = 0.

A rational function can be represented by a polynomial that has been divided by another polynomial. The set of all numbers omitting the zeros in the denominator makes up the domain of a rational function because polynomials are defined everywhere. First example: x = f(x) (x - 3).

A) Factor the denominator and numerator together:

w(x) = 3(x - 7)/(3x + 1) = (3x - 21)/(3x2 - 20x - 7) (x - 7)

B) Locate the discontinuity point, if one exists:

With x - 7 = 0 or 3x + 1 = 0, the denominator is 0. As a result, the function exhibits discontinuity points at x = -7 and x = -1/3.

C) Identify the vertical asymptote: For x = -1/3, the function has a vertical asymptote.

D) Locate the horizontal asymptote: The numerator and denominator each have degrees of 2 and 1, respectively. As a result, the horizontal asymptote is y = 0.

E) Visualize the function

Using the value table:

x y

-5 4.5

-2 -1.4

-0.4 -4.11

0 -7

1 -2.4

5 -0.5

7 undefined

The horizontal asymptote at y = 0 and the vertical asymptote at x = -1/3 can also be plotted.

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