Ben draws an irregular pentagon.
The interior angles of the pentagon
he has drawn are all less than 180°.
Ben attempts to express the
interior angles of his pentagon
using algebra.
His expressions are

xᵒ, (x +40)°, (2x − 30)°,
3(x - 40) and 3xº

Show that Ben is incorrect.
Input note: include the angle sum
of a pentagon, the value of x and
the size of any angles that don't
meet the criteria set out in the
question.


Ben is incorrect because…

The number of adult tickets that were sold would be = 435 tickets.

A ticket is an official document that gives an individual access to an event.

The cost of adult tickets = $8

The cost for student tickets = $4

The number of students tickets sold = X

The number of adults tickets sold = X +30

The told number of tickets sold = 840

To find X;

X + X + 30 = 840

2x + 30 = 840

2x = 840-30

2x = 810

X = 810/2

X = 405

Therefore, the number of tickets sold for adults = 405 +30 = 435 tickets.

Learn more about tickets here:

https://brainly.com/question/25333829

#SPJ1

Answer:

246.5

Step-by-step explanation:

86275÷35

= 246.5

approximately 247

Answer:

-21

Step-by-step explanation:

9/1 x -7/2 = -42/2 = -21

The probability that more than 20% of the sample are from poverty households is approximately 0.8365.

What is the probability?

Probability is simply how likely something is to happen. Whenever we're unsure about the outcome of an event, we can talk about the probabilities of certain outcomes—how likely they are. The analysis of events governed by probability is called statistics.

We can use the normal approximation to the binomial distribution to solve this problem, given that the sample size is relatively large (n=300) and the probability of success (p=0.22) is not too close to 0 or 1.

Let X be the number of children in the sample who live in poverty households. Then X follows a binomial distribution with parameters n=300 and p=0.22.

The mean of X is given by μ = np = 300 x 0.22 = 66, and the standard deviation is σ = sqrt(np(1-p)) = sqrt(300 x 0.22 x 0.78) ≈ 6.23.

We want to find the probability that more than 20% of the sample are from poverty households, which is equivalent to finding P(X > 0.2n) = P(X > 60).

To use the normal approximation, we can standardize X as follows:

Z = (X - μ) / σ

Then, we have:

P(X > 60) = P(Z > (60 - 66) / 6.23) ≈ P(Z > -0.96)

Using a standard normal table or calculator, we can find that the probability of Z being greater than -0.96 is approximately 0.8365.

Therefore, the probability that more than 20% of the sample are from poverty households is approximately 0.8365.

To learn more about the probability visit:

https://brainly.com/question/13604758

#SPJ1

The two states are Arizona and New Mexico.

Arizona and New Mexico are two states with unique demographics that differ from the rest of the United States.

Thus, these states are characterized by a high Latino population and, in addition, a high percentage of native population. This, due to its proximity to the border with Mexico.

Thus, Arizona has counties like Apache County, where 70% of its population is native; and like Yuma County, where 51% of its population is Hispanic.

In turn, New Mexico has counties like McKinley County, where 75% of its population is native; and as Hidalgo County, where 55% of its population is Hispanic.

Learn more about demographics in https://brainly.com/question/7212745

Answer: Your screenshot

Step-by-step explanation:

is insufficient

The key to this problem is to identify the functions; isolate the functions dependent on only x; and define each function in terms of x. Once every function is in terms of x then we can apply them to the equation that needs to be solved. Identify the functions: Here we are given four functions f(x); g(x); h(x); and i(x) so anytime we see these letters appear in an equation is where we would substitute the function. Isolate the functions dependent on only x: At a glance we can tell that only g(x) is purely in terms of x, every other function contains another function within their equations.

Define each function in terms of x: Since g(x) is in terms of x and i(x) contains g(x) then we can substitute 3x+4 for g(x) making i(x)=(x-2)*(3x+4) which then simplifies to i(x)=3x2-2x-8

Since h(x) contains i(x) then we can substitute the i(x) we made in 3a to get h(x)=3x2-11-(3x2-2x-8) which then simplifies to h(x)=2x-3

Since f(x) contains g(x) and h(x) then we can substitute those equations to get f(x)=2(3x+4)-(2x-3) which then simplifies to f(x)=4x+11

Now we apply our defined equations to the equation in question. There are two ways to do this, we can either apply our x values to each individual equation first or make the equation in question in terms of x. In this case I will make the equation in terms of x first. The first part of this process is understanding that the ° symbol does not represent degrees in this case, it represents the substitution of a function into another function. For example, if you saw (f°g)(x) then you would take the equation for g(x) and substitute it for every x value in the f(x) equation. Based on the process around ° it would be best to start from i(x) and work backwards to f(x) then h(x). So 2i=2(i(x))=2(3x2-2x-8)=6x2-4x-16       Ignoring the 3 we then evaluate f°2i=f(2(i(x)))=4(6x2-4x-16)+11=24x2-16x-64. Then we multiply the 3 to get 3f°2i=3(24x2-16x-64)=72x2-48x-192

Then we get to h°3f°2i=2(72x2-48x-192)-3=144x2-96x-384 which can simplify to 48(3x2-2x-8) or 48(3x+4)(x-2).

Finally we can divide g(x) making (h°3f°2i÷g)(x)=(48(3x+4)(x-2))/(3x+4)=48(x-2)

With the final equation in terms of only x we can finally solve by substituting each x value, giving us -288 when x=-4; -240 when x=-3; and 0 when x=2.

Answer:

f'(x) = 2ax + b

Step-by-step explanation:

Differentiate each term using the power rule

\(\frac{d}{dx}\) (a\(x^{n}\) ) = na\(x^{n-1}\)

Given

f(x) = ax² + bx , then

f'(x) = 2a\(x^{2-1}\) + b\(x^{1-1}\)

     = 2ax + b\(x^{0}\) ( \(x^{0}\) = 1 )

     = 2ax + b

Hence, OC bisects AB, as congruent parts of congruent triangles are equal.

When two or more geometric figures are similar in size, form, and orientation, this is referred to as congruency in geometry. Two figures can be overlaid on one another by translation, rotation, and/or reflection when they are congruent because they are almost similar to one another and do not alter in size, form, or orientation.

For the given problem, the complete steps of proof with reasoning are:

(a) OC is perpendicular to AB in circle O (given). i.e ∠OCA and ∠OCB are right angles.

Reason: This is given in the problem statement. It establishes that OC forms a right angle with AB at point C in circle O. i

(b) Draw OA and OB (construction).

Reason: This is a construction step that introduces radii OA and OB from the center O of the circle to points A and B on the circle. This sets up the framework for the subsequent steps and establishes the positions of A and B in relation to the circle and the perpendicular OC.

(c) OA = OB (radii of the same circle are equal).

Reason: Radii of the same circle are always equal in length. This is a basic property of circles, where all radii have the same length, which can be stated as OA = OB based on the definition of a circle.

(d) OC = OC (Reflexive Property of Equality)

Reason: It is a property of line segments that they are equal to themselves. This is known as the Reflexive Property of Equality, which states that any quantity is equal to itself.

(f) AC = BC (common side of congruent triangles).

Reason: AC and BC are line segments that are both radii of the same circle, and OA = OB (Step c). Therefore, by the definition of congruent segments, AC = BC.

(e) Triangle ACO is congruent to triangle BCO (HL congruence criterion for right triangles).

Reason: Angle ACO and angle BCO are both right angles based on the given information that OC is perpendicular to AB (Step a). Also, AC = BC (Step d) and OA = OB (Step c). Therefore, by the Hypotenuse-Leg congruence criterion for right triangles, triangle ACO is congruent to triangle BCO.

(g) OC bisects AB (congruent parts of congruent triangles are equal).

Reason: Since triangle ACO is congruent to triangle BCO (Step e), the corresponding parts of congruent triangles are equal. In this case, OC is a common side (hypotenuse) of both triangles, and AB is a side of both triangles. Therefore, by the definition of a segment bisector, OC bisects AB.

Learn more about congruency here:

https://brainly.com/question/7888063

#SPJ1

Answer: $22.00

Steps: Miss Sally received $22.00 as her tip. Multiply 110 by .20 to find the percent she received.

plz mark brainliest:)

Answer:

a=9, b=45, c=31.5, d=18, f=27

Step-by-step explanation:

To find the value of a, you can take 72-54=18 and do 18/2=9

a=9

To find the value of b, you can multiply the three a's. 27 is the product of the 3 a's. Next, you will do 72-27 to find the value of b

b=45

To find the value of c, you can take 9 and subtract it from 72, or in other words: 72-9=63. You will then divide 63/2 to find the value of c

c=31.5

To find the value of d, you can multiply (9*4)=36. You can then take 72-36 and get 36. To find the value of d, you will then divide 36/2.

d=18

To find F, you are given a clue that 1 a and 1 d together=f.

9+18=f

f=27

Answer:

a=9

b=36

c=45

d=31.5

f=40.5

Step-by-step explanation:

Phew! that was pretty tough. But I solved it! Your welcome! :)

Answer:

I think it would be Maxine's, since they did more tests.

There are nC2 different votes possible, where n is the number of bands on the list and nC2 represents the number of ways to choose 2 bands out of n.

To calculate nC2, we can use the formula for combinations, which is given by n! / (2! * (n-2)!), where ! represents factorial.

Let's say there are m bands on the list. The number of ways to choose 2 bands out of m can be calculated as m! / (2! * (m-2)!). Simplifying this expression further, we get m * (m-1) / 2.

Therefore, the number of different votes possible is m * (m-1) / 2.

In the given scenario, we don't have the specific number of bands on the list, so we cannot provide an exact number of different votes. However, you can calculate it by substituting the appropriate value of m into the formula m * (m-1) / 2.

Know more about factorialhere:

https://brainly.com/question/18270920

#SPJ11

To find the linear approximation l(x) of the function f(x) = cos(x) at a = 2π/3, we'll use the formula:
l(x) = f(a) + f'(a)(x - a)
Here, f(a) is the function value at a, and f'(a) is the derivative of the function at a.
First, find f(a): f(2π/3) = cos(2π/3) = -1/2
Next, find f'(x): The derivative of cos(x) is -sin(x). Thus, f'(a) = f'(2π/3) = -sin(2π/3) = -√3/2

Now, substitute these values into the linear approximation formula:
l(x) = -1/2 - (√3/2)(x - 2π/3)
This is the linear approximation of the function f(x) = cos(x) at a = 2π/3.

To find the linear approximation of the function f(x)=cos(x) at a=2π/3, we need to first find the value of the function and its derivative at a=2π/3.
f(2π/3) = cos(2π/3) = -1/2
f'(x) = -sin(x)

Then, we can use the linear approximation formula:
l(x) = f(a) + f'(a)(x-a)

Plugging in the values, we get:
l(x) = (-1/2) + [-sin(2π/3)](x-2π/3)

Simplifying, we get:
l(x) = (-1/2) - (√3/2)(x-2π/3)

Therefore, the linear approximation of f(x) = cos(x) at a=2π/3 is l(x) = (-1/2) - (√3/2)(x-2π/3).

Learn more about Functions:

brainly.com/question/12431044

#SPJ11

Answer:

256 DIVIDE BY 8 THEN PLUS 1

Step-by-step explanation:

==========================================

Explanation:

AB is a diameter of the circle with point O in the center. This makes angle AOB to be 180 degrees. Consequently, arc ADB makes up 180 degrees of a full 360 degree circle (ie it makes up half of the circle since 180/360 = 1/2)

We're told that arc ADB is 15pi units long. Since arc ADB makes up half the circle, the full circle must therefore be 2*15pi = 30pi. This is the circumference.

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

We're also told that angle COB is 60 degrees. Let's find angle COA

(angleCOA) + (angleCOB) = 180

angleCOA = 180-(angleCOB)

angleCOA = 180-60

angleCOA = 120

Angle COA is 120 degrees

This makes up 120/360 = 1/3 of the full circle

So (1/3)*(circumference) = (1/3)*(30pi) = 10pi is the arc length of AC where we take the shorter path from A to C along the circle's edge.

Answer:

AC = 10π

Step-by-step explanation:

Consider arc ADB with length 15π

ADB = circumference of circle × fraction of circle , that is

2πr × \(\frac{180}{360}\) = 15π

2πr × \(\frac{1}{2}\) = 15π

πr = 15π ( divide both sides by π )

r = 15

∠ AOC = 180° - 60° = 120° ( adjacent angle to 60° )

Thus

AC = 2πr × \(\frac{120}{360}\)

     = 2π × 15 × \(\frac{1}{3}\)

     = 30π × \(\frac{1}{3}\)

     = 10π

Answer:

12

Step-by-step explanation:

(5×6)-½(3×6 + 2×4 + 2×5)

=30 - ½(18+8+10)

= 30 - ½(36)

=30-18= 12

Answer:

87 I am getting points yayyyy

Answer:

7z

Step-by-step explanation:

Answer: 7z

Step-by-step explanation:

two negatives cancel into a positive, so -(-3z) is +3z. 4z + 3z = 7z

Answer:

$3.97x + $10 < (or equal to) $25

Step-by-step explanation:

Answer:

3.97x+10\(\leq\)25

Step-by-step explanation:

3.97 per burger (x) + 10 for delivery fee will be less than or equal to 25.

Answer:

Fred scored 100
Bob scored 50
Gladys scored 20

Step-by-step explanation:

Fred = 50% * 200
        = 50/100 * 200
        = 0.5 * 200
        = 100

Bob  = 25% * 200
        = 25/100 * 200
        = 0.25 * 200
        = 50

Gladys = 10% * 200
            = 10/100 * 200
            = 0.1 * 200
            = 20

The identities among the given statements are:

tan x = sin x / cos x

sin x / tan x = cos x

We have,

Let's analyze each of the given statements to determine whether they are identities:

tan x = sin x / cos x:

This is an identity.

It is known as the fundamental identity of trigonometry, as it holds true for all values of x (except when cos x is equal to 0).

tan x cos x = sin x:

This is not an identity.

It is a specific equation that may be true for certain values of x, but it does not hold true for all values of x.

cos x = tan x sin x:

This is not an identity.

Similar to the previous statement, it is a specific equation that may be true for certain values of x, but it does not hold true for all values of x.

sin x / tan x = cos x:

This is an identity.

It can be derived from the fundamental identity by dividing both sides by cos x, resulting in sin x / cos x = cos x / cos x, which simplifies to sin x / tan x = cos x.

Thus,

The identities among the given statements are:

tan x = sin x / cos x

sin x / tan x = cos x

Learn more about trigonometric identities here:

https://brainly.com/question/14746686

#SPJ1

Hey there! I'm happy to help!

This does not satisfy the equation y=x as x and y have two different values. 0 and 3 are not equal. A point like (3,3) would satisfy that equation.

Have a wonderful day! :D

Answer:

  (x, y) = (2, 4)

Step-by-step explanation:

You want to solve the system of equations ...

There are numerous ways to solve this system of equations. One of the simplest is to use a graphing calculator. (See the attachment)

  (x, y) = (2, 4)

The second equation gives an expression for x that can be substituted into the first equation:

  y = -2(y -2) +8

  3y = 12 . . . . . . . . add 2y and simplify

  y = 4

  4-2 = x = 2

The solution is (x, y) = (2, 4).

The y-variable has a coefficient of 1 on the left side of the equal sign, so we can eliminate the y-variable by subtracting the second equation from the first.

  (y) -(y -2) = (-2x+8) -(x)

  2 = -3x +8 . . . . . . . . . . . simplify

  3x = 6 . . . . . . . . . . add 3x-2

  x = 2 . . . . . . . . divide by 3

  y = -2(2) +8 = 4 . . . . . substitute for x in the first equation

The solution is (x, y) = (2, 4).

Neil can sue Perry and the Oil Shop for breach of an implied warranty of fitness for a particular purpose

Poor compression of both fuel and air inside a car engine is a recipe for disaster. The most common reasons for poor engine combustion is due to broken valve seals, holes within cylinders and overused piston rings, forcing air to leak out. One of the easier engine faults to diagnose is leaking engine coolant

To learn more about engine trouble from the given link

https://brainly.com/question/18428188

#SPJ4

To prove that YEAR is a square, we need to show that all four sides have the same length and all four angles are right angles (90 degrees).

Side Lengths: To find the lengths of the sides, we can use the distance formula:

d = √((x2 - x1)² + (y2 - y1)²)

For example, to find the length of the side that connects Y and E, we can use the following calculation:

d = √((3 - 1)² + (0 - (-4))²) = √((2)² + (4)²) = √(4 + 16) = √20

We can use the same formula to calculate the lengths of the other sides. By doing so, we will find that the length of all four sides are the same, which is √20. This means that all four sides of YEAR are congruent, and therefore it is a square.

Based on the following data: rRF=5.5%;rM−rRF=6%;b=0.8;D1=$1.00;P0=$25.00;g=6%;rd= firm's bond yield =6.5%, the firm's cost of equity using the CAPM approach is 10.3%.

To calculate the firm's cost of equity using the CAPM (Capital Asset Pricing Model) approach, we use the following formula:

Cost of Equity (re) = rRF + (rM - rRF) * β

Given: Risk-free rate (rRF) = 5.5% Market risk premium (rM - rRF) = 6% Beta (β) = 0.8

Using the provided data, we can calculate the firm's cost of equity:

Cost of Equity = 5.5% + (6% * 0.8) = 5.5% + 4.8% = 10.3%

Therefore, the firm's cost of equity using the CAPM approach is 10.3%.

To know more about cost , visit

https://brainly.com/question/32842885

#SPJ11

To determine the minimum number of terms we need to add in order to find the sum of the series with an error less than 0.0001, we can use the Alternating Series Estimation Theorem.

The Alternating Series Estimation Theorem is a useful tool for approximating the sum of an alternating series and determining the accuracy of the approximation. An alternating series is a series in which the terms alternate in sign, such as (-1)^n or (-1)^(n+1).

To use the Alternating Series Estimation Theorem, we need to check two conditions. Firstly, we verify that the series is convergent, meaning that the partial sums of the series approach a finite limit as the number of terms increases. If the series is not convergent, this estimation method cannot be applied.

Once we have established that the series is convergent, we can use the theorem to determine the minimum number of terms required to achieve a desired level of accuracy. The theorem tells us that the error in approximating the sum of the series using a partial sum is less than or equal to the absolute value of the first omitted term.

In our case, we want the error to be less than 0.0001. By finding the absolute value of the first omitted term, we can determine how many terms we need to add to the partial sum in order to achieve this desired level of accuracy. This will give us the minimum number of terms required to obtain the sum with an error less than 0.0001.

Learn more about the Alternating Series

brainly.com/question/30400869

#SPJ11