the midpoints of the sides of a regular hexagon abcdef are joined in order to form a smaller regular hexagon. what fraction of the area of abcdef is enclosed by the smaller hexagon?

Profit function is P(x) = 3.1x - 0.05x² - 181

The profit a business makes is equal to the revenue it takes in minus what it spends as costs. To obtain the profit function, subtract costs from revenue.

P(x) = R(x) - C(x)

Given,

Cost C(x) = 181 +2.9x

Revenue R(x) = 6x -0.05x²

Profit P(x) = R(x) - C(x)

                = 6x - 0.05x² - (181 +2.9x)

                = 6x - 0.05x² - 181 - 2.9x

         P(x) = 3.1x - 0.05x² - 181

Hence,  P(x) = 3.1x - 0.05x² - 181 is the profit function.

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The X value for the boundary for the lowest 2.5% of a normal distribution with a mean of 50 and a standard deviation of 4 is 43.04.

The lowest 2.5% boundary for a normal distribution with a mean of 50 and standard deviation of 4 can be calculated using the Z-score formula.

Z = (X - mean) / standard deviation

We want to find the X value for which Z = -1.96 since -1.96 represents the boundary for the lowest 2.5% of a standard normal distribution.

Plugging in the mean and standard deviation:

-1.96 = (X - 50) / 4

Solving for X:

X = 50 - 1.96 × 4

X = 43.04

So, the X value for the boundary for the lowest 2.5% of a normal distribution with a mean of 50 and a standard deviation of 4 is 43.04.

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The speed of the slower boat is 15 mph and the speed of the faster boat is 35 mph.

The problem involves using the formula for distance, speed, and time, which is:

distance = speed × time

In this case, we are given the distance between two boats (400 miles) and the time it takes for them to meet (8 hours), and we need to find the speed of each boat. This involves solving a linear equation to find the unknown speed. The problem also involves the concept of finding the rate of change of distance, which is the sum of the speeds of the two boats.

Let's call the speed of the slower boat = x mph.

The speed of the faster boat would be = x + 20 mph.

The distance between the two boats decreases at a rate = x + x + 20 = 2x + 20 mph.

The time it takes for the two boats to meet is 8 hours, so the distance between the two boats when they meet is:

400 = (2x + 20) × 8

Solving for x:

400 = 16x + 160

16x = 240

x = 15

So, the speed of the slower boat is 15 mph and the speed of the faster boat is x + 20 = 35 mph.

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The length of the similar polygon is as follows:

GK = 30 units

TU = 24 Units

Two polygons are similar if their corresponding angles are congruent and their corresponding sides are in proportion.

Therefore, the corresponding angles of the polygons are congruent and the sides are in ratio of each other.

Hence, let's find the side GK and TU as follows:

QRSTU ~ IJKGH

Therefore,

24 / GK = 16  /20

cross multiply

16GK = 480

GK = 480 / 16

GK = 30 Units

Hence,

TU  / 30 = 16 / 20

cross multiply

20 TU = 480

TU = 480 / 20

TU = 24 Units

Therefore,

GK = 30 units

TU = 24 units

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The required angle is 26.5°, line y=1/2x + 1 made with an x-axis.

The slope of the line is a tangent angle made by line with horizontal. i.e. m =tanx where x in degrees.

Here,
Given the equation of the line,
y = 1/2x + 1

Compare the above equation with equation y = max +c
m = 1/2

tanФ = 1/2   [since m = tanФ]
Ф = tan⁻¹[1/2]
Ф = 26.5°

Thus, the required angle is 26.5°.

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Answer:

-1/3

Step-by-step explanation:

multiply across

1/2 * -2/3

-2/6

-1/3

The probability that at most one car has any surface flaws is 0.0067.

The formula to calculate the surface flaws will be -

P(X = 0) = [tex] {e}^{- lambda} {lambda}^{X} [/tex]/X!, where lambda is the mean of Poisson random variable with mean. It is 5 according to the question. Now keeping the values in formula to find the probability.

P = [tex] {e}^{- 5} {5}^{0} [/tex]/0!

As exponent 0 will be considered 1 and factor of the 0 is 0. So, rewriting the equation -

P = [tex] {e}^{- 5} [/tex]

Finding the value now

P = 0.0067

Thus, the probability is 0.0067.

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The complete question is -

The number of surface flaws in plastic panels used in the interior of automobile has a Poisson distribution with a man of 0.05 flaws per square foot of plastic panel. Assume an automobile interior contains 10 square feet of plastic panel.

if 10 cars are sold to a rental company, what is the probability that at most 1 car has any surface flaws?

The area of the surface generated when the given curve is revolved about the x-axis with y=8√x on [9,20] is approximately 764.26 square units.

The area of the surface generated when the given curve is revolved about the x-axis is calculated using the formula:

A = 2 * π * ∫[a,b] y * √(1 + (dy/dx)²) dx,

where y = 8√x, and a and b are the limits of integration, i.e., a = 9, and b = 20.

First, we'll find the derivative of y with respect to x:

dy/dx = 8 / (2 * √x)

Now, we can substitute the values into the formula:

A = 2 * π * ∫[9,20] 8√x * √(1 + (8 / (2 * √x))²) dx

Using the change of variable u = √x, the above equation becomes:

A = 16π * ∫[3,4.472] u² * √(1 + (8 / u)²) du

Evaluating the definite integral, we get:

A = 16π * (u³ / 3) * √(1 + (8 / u)²) |[3,4.472]

A = 16π * [(4.472³ / 3) * √(1 + (8 / 4.472)²) - (3³ / 3) * √(1 + (8 / 3)²)]

A = 16π * [(4.472³ / 3) * √(1 + (8 / 4.472)²) - (27 / 3) * √(1 + (8 / 3)²)]

A ≈ 764.26

So, the area of the surface generated when the given curve is revolved about the x-axis is approximately 764.26 square units.

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This indicates that the cutoff value for the amount of minutes before contacting the consumer is 674 minutes, rounded to the closest minute.

Quartiles are three numbers that divide sorted data into four equal portions with an equal amount of observations each. A quantile is a sort of quantile. The first quartile is sometimes known as the lower quartile or Q1. Second quartile: Also known as the median or Q2. Third quartile: Also known as the higher quartile or Q3.

Here,

To find the upper fence, we need to calculate the following statistics:

Q1 (first quartile), Q2 (median), and Q3 (third quartile) of the data

Interquartile range (IQR), which is the difference between Q3 and Q1

Upper fence, which is Q3 + 1.5 * IQR

First, we need to order the data in ascending order:

339, 350, 358, 388, 430, 458, 458, 463, 480, 489, 501, 536

Next, we can find the quartiles:

Q1 = 388

Q2 = 458

Q3 = 501

IQR = Q3 - Q1 = 501 - 388 = 113

Finally, we can calculate the upper fence:

Upper fence = Q3 + 1.5 * IQR = 501 + 1.5 * 113 = 674

This means that the cutoff point for the number of minutes at which the customer should be contacted is 674 minutes, rounded to the nearest minute.

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Answer: (-3, -1/2)

Step-by-step explanation: Search math w ay on the internet for any further math questions :)

x=-10, 2

you would have to factor it.

refer to picture

When the sample size is decreased from 39 to 29 , the impact on confidence interval will be (c) It would become wider due to using the t distribution.

we know that , in general, as the sample size decreases, the variability of the estimate increases and the width of the confidence interval becomes larger.

The t distribution is used when the sample size is small, which increases the width of the confidence interval to account for the greater uncertainty in the estimate.

When the sample size is large, the t distribution approaches the standard normal (z) distribution, which results in a narrower confidence interval.

Therefore, a decrease in sample size would result in a larger t distribution and a wider confidence interval.

The given question is incomplete , the complete question is

In a situation where the sample size was decreased from 39 to 29, what would be the impact on the confidence interval ?

(a) It would become narrower with fewer values.

(b) It would remain the same as sample size does not impact confidence intervals.

(c) It would become wider due to using the t distribution.

(d) It would become narrower due to using the z distribution.

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The lateral surface area of the rectangular prism given in the picture is 36 cm ²

The lateral surface area of a rectangular prism can be found by the formula :

= 2 x height x ( Length + Breadth )

Height = 2 cm

Length = 3 cm

Breadth = 6 cm

The lateral surface area is therefore:

= 2 x 2  x ( 3 + 6 )

= 4 x 9

= 36 cm ²

In conclusion, the lateral surface area is 36 cm ².

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The new coordinate of the points after the dilation will be (3, 5).

Dilation is the process of increasing the size of an item without affecting its form. Depending on the scale factor, the object's size can be raised or lowered. There is no effect of dilation on the angle.

The point is (6, 10). And the scale factor is 1/2. Then the new coordinate of the points after the dilation is given as,

⇒ (1/2)(6, 10)

⇒ (1/2 x 6, 1/2 x 10)

⇒ (3, 5)

The new coordinate of the points after the dilation will be (3, 5).

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By thoroughly reacting a 2.2g zinc nail with an excess of hydrochloric acid, 0.0075 L of hydrogen gas is created.

The force per unit area on an item in the fluid or on the surface of a closed container is measured as fluid pressure. Gravity, acceleration, or forces outside a closed container can all create this pressure. Because a fluid has no fixed structure, its pressure is applied in all directions.

Here,

The reaction between zinc and hydrochloric acid produces hydrogen gas according to the following equation:

Zn + 2HCl -> ZnCl2 + H2

From the equation, we can see that 1 mole of zinc reacts with 2 moles of hydrochloric acid to produce 1 mole of hydrogen gas. The volume of a gas is proportional to the number of moles at constant temperature and pressure, so if we can determine the number of moles of zinc that were reacted, we can calculate the volume of hydrogen produced.

The moles of zinc can be calculated using the molar mass of zinc:

moles = mass / molar mass

moles = 2.2 g / 65.38 g/mol = 0.0337 mol

Since 1 mole of zinc reacts with 2 moles of hydrochloric acid, the number of moles of hydrogen produced is 0.0337 mol * 1 mol H2/1 mol Zn = 0.0337 mol H2.

Finally, the volume of hydrogen produced at standard temperature and pressure (STP) is calculated using the Ideal Gas Law:

PV = nRT

V = nRT / P

V = (0.0337 mol) * (0.08206 L atm / K mol) * (273.15 K) / (1 atm)

V = 0.0075 L

0.0075 L of hydrogen gas are produced by completely reacting a zinc nail with a mass of 2.2g with an excess of hydrochloric acid.

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Complete question:

What volume of hydrogen gas are produced by completely reacting a zinc nail with a mass of 2.2g with an excess of hydrochloric acid?

An equation for Windy Kite's total cost, y, in terms of the number of kites purchased, x, is y = 2x + 20.

An equation for Kites-R-Fun's total cost, y, in terms of the number of kites purchased, x, is y = 4x + 8.

Based on the table, if the Alaskan customer wants to buy 4 kites, Kites-R-Fun charges the least.

If the Alaskan customer wants to buy 10 kites, Windy kites charges the least.

The solution to the system of equations is (6, 32).

The meaning of the solution is that 6 kites would cost a total of $32 at both Windy kites and Kites-R-Fun.

In order to write a linear equation to describe this situation, we would a assign variable to the number of kites purchased and the total cost respectively, and then translate the word problem into a linear equation as follows:

Since Wendy charges $2 per kite and a flat rate of $20 for shipping, a linear equation that models the total cost is given by:

y = 2x + 20

When x = 4, the total cost for Windy kites is given by:

y = 2(4) + 20

y = $28.

When x = 7, the total cost for Windy kites is given by:

y = 2(7) + 20

y = $34.

When x = 10, the total cost for Windy kites is given by:

y = 2(10) + 20

y = $40.

For Kites-R-Fun, a linear equation that models the total cost is given by:

y = 4x + 8

When x = 4, the total cost for Kites-R-Fun is given by:

y = 4(4) + 8

y = $24.

When x = 7, the total cost for Kites-R-Fun is given by:

y = 4(7) + 8

y = $36.

When x = 10, the total cost for Kites-R-Fun is given by:

y = 4(10) + 8

y = $48.

Lastly, we would use an online graphing calculator to plot the system of linear equations as shown in the graph attached below.

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(C) $563,700 in cash was received from customers during the year.

Accounting lingo for partial payment of an amount outstanding is "on the account."

The phrase "on account" can also refer to buying or selling anything on credit.

On credit is another way to say "on the account."

Simply changing a sales representative's job title won't make them an account manager.

The needed abilities are varied.

Account managers require abilities in project management, financial control, consultative/value selling, and planning, some of which may require training.

So, gross sales of $560,000.

Accounts receivable decreased ($22,500 - $18,800). $3,700.

Money obtained from clients. $563,700.

Note that the further details provided in the question are not necessary to determine the total amount of money received from customers for the year.

Therefore, (C) $563,700 in cash was received from customers during the year.

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The total number of ways are 225, 225.

Combinations are mathematical operations that count the number of potential configurations for a set of elements when the order of the selection is irrelevant. You can choose the components of combos in any order. Permutations and combinations can be mixed up.

Given:

There are 11 kittens and 15 puppies.

so, we have to select 3 kittens from 11 kittens and 4 puppies from 15 puppies.

Then, the number of ways can be

= C(11, 3) x C(15, 4)

= 990 / 6 x 32,760/ 24

= 165 x 1365

= 225, 225.

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Answer:

19) x=10⁰ 20) x=17⁰

Step-by-step explanation:

19) angles in a straight line add upto 180⁰

 6x-10⁰+4x⁰+6+7x+14⁰=180⁰

collect like terms

 17x+10⁰=180⁰

 17x=1170⁰

x=10⁰

20)58⁰ alternates with 4x-10 therefore;

4x-10⁰=58⁰

4x=58⁰+10⁰

4x=68⁰

x= 17⁰

Answer:

the probability becomes less

Step-by-step explanation:

In total, there are 192 + 144 + 144 = 480 different starting lineups that can be created.

There are 3 centers to choose from, and for each center there are 4 choices for each of the two guard positions and 4 choices for each of the two forward positions. So, there are:

3 * 4 * 4 * 4 = 192

different starting lineups without x.

Lineups with x as guard: There are 3 centers, 3 choices for the first guard (since x can play either guard or forward), 4 choices for the second guard, and 4 choices for each forward. So, there are

3 * 3 * 4 * 4 = 144

different lineups with x as guard.

Lineups with x as forward: There are 3 centers, 4 choices for each guard, 3 choices for the first forward (since x can play either guard or forward), and 4 choices for the second forward. So, there are 3 * 4 * 3 * 4 = 144 different lineups with x as forward.

In total, there are 192 + 144 + 144 = 480 different starting lineups that can be created.

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The number of students will be equal to LCM which is 24.

Given:- A certain number of students can be arranged in groups of 3,4,6or 8 with no student left behind.

To find:- The number of students.

Solution:- To find minimum number of students need to find LCM (3,4,6,8).

[tex]3=3^{1}[/tex]

[tex]4=2*2=2^{2}[/tex]

[tex]6=2*3=2^{1} *3^{1}[/tex]

[tex]8=2*2*2=2^{3}[/tex]

LCM: Least common multiplier of given numbers is the Leastmultiplier number which is given perfectly divisible by the given numbers.

LCM= product of eac factor of highest power.

LCM=[tex]2^{3} *3^{1} =8*3=24[/tex]

Hence, minimum number of students= 24 or students are multiple of 24.  

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The rate of change of the volume of the cone at the given instant is 1 238 768 66.67 cm^3/s.

The volume of a cone can be calculated using the formula V = (πr^2h)/3, where r is the radius and h is the height of the cone.

At the given instant, radius = 8 88 cm and height = 10 1010 cm.

Substituting these values in the formula we get,

[tex]V = (π(8 88 cm)^2(10 1010 cm))/3 = 2 477 537 33.33 cm^3[/tex]

The rate of change of the volume of the cone at that instant can be calculated as follows:

Let dV/dt be the rate of change of the volume at that instant.

[tex]dV/dt = (dV/dr)*(dr/dt) + (dV/dh)*(dh/dt) \\dr/dt = 3 33 cm/s \\dh/dt = -4 44 cm/s[/tex]

Differentiating the volume of a cone formula with respect to r and h, we get

[tex]dV/dr = (πr^2h) dV/dh = (πr^2h)/3[/tex]

Substituting these values in the equation for dV/dt, we get

[tex]dV/dt = (π(8 88 cm)^2(10 1010 cm)) + (π(8 88 cm)^2(10 1010 cm))/3 * (-4 44 cm/s) = 1 238 768 66.67 cm^3/s[/tex]

Therefore, the rate of change of the volume of the cone at the given instant is [tex]1 238 768 66.67 cm^3/s[/tex].

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The perimeter of this triangular park is equal to: 3x² 37x - 4 feet.

Mathematically, the perimeter of a triangle can be calculated by using this mathematical expression:

P = a + b + c

Where:

P represents the perimeter of a triangle.

a, b, and c represents the length of sides of a triangle.

Substituting the given parameters into the perimeter of a triangle  formula, we have the following;

Perimeter of triangle, P = 12x + (15x + 4) + (10x + 3x² - 8)

Perimeter of triangle, P = 12x + 15x + 4 + 10x + 3x² - 8

Perimeter of triangle, P = 3x² 37x - 4 feet.

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If we select three balls, the probability of selecting exactly one white one is 16.

There are 6 balls in a box.

2 white and 4 black.

If we select three balls, then we have to determine the probability of selecting exactly one white.

First we determine the number of ways of selecting three balls in total of 6 balls. So

[tex]^{6}C_{3} = \frac{6!}{3!(6-3)!}[/tex]

[tex]^{6}C_{3} = \frac{6!}{3!3!}[/tex]

[tex]^{6}C_{3} = \frac{6\times5\times4\times3!}{3\times2\times1\times3!}[/tex]

Simplify

[tex]^{6}C_{3}[/tex] = 5 × 4

[tex]^{6}C_{3}[/tex] = 20

Now determining the probability of selecting the 3 balls out of non white balls.

[tex]^{4}C_{3}=\frac{4!}{3!(4-3)!}[/tex]

[tex]^{4}C_{3}=\frac{4!}{3!1!}[/tex]

Simplify

[tex]^{4}C_{3}=\frac{4\times3!}{3!\times1}[/tex]

[tex]^{4}C_{3}[/tex] = 4

Now, the probability of selecting exactly one white one = The number of ways of selecting three balls in total of 6 balls - The probability of selecting the 3 balls out of non white balls

The probability of selecting exactly one white one = 20 - 4

The probability of selecting exactly one white one = 16

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Answer:

Below

Step-by-step explanation:

You cannot 'solve' this equation..... you have only one equation and TWO unknowns p and x      you will need another equation relating p and x to solve this

The inverse of the functions y = x + 3 and y = 2x - 4 are y = x - 3 and

y = (x + 4)/2 respectively.

A function can be defined as the outputs for a given set of inputs.

The inputs of a function are known as the independent variable and the outputs of a function are known as the dependent variable.

Given, A function y = x + 3 or f(x) = x + 3.

Now, To find the inverse of f(x) we'll solve for 'x' in terms of 'y'.

y = x + 3.

x = y - 3.

y = x - 3.

f⁻¹(x) = x - 3.

Again,

y = 2x - 4.

2x = y + 4.

x = (y + 4)/2.

y = (x + 4)/2.

f⁻¹(x) = (x + 4)/2.

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Answer:

What are we looking to solve for?

How much each shirt she bought for the fundraiser costs, each.

What variable can be used to represent the unknown?

The variable "t".

What is the equation to solve the variable?

You can use the following equation as a framework for solving:

t * 22 = 231 solve for t.

Now lets solve:

I am going to use inverse operations: Divide instead of multiply.

231/22 = 10.05

Each shirt is worth $10.50.

Step-by-step explanation:

Hope it helps! =D

Answer:

We want to know how much each t-shirt costs.

t = 10.50

Step-by-step explanation:

We want to know how much each t-shirt costs.

Let the cost of each t-shirt  = t

22 * t = 231

Divide each side by 22

22t/2 = 231/22

t = 10.50

The cost of each t-shirt is 10.50

The equation represents the relationship between the independent variable, x, and the dependent variable is y= 2x

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

The table of values

On the yable of values, we can see that

y is twice of x

When represented as an equation, we have

y = 2x

Hence, the equation is y = 2x

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