Find the slope of the line whose equation is 5y = x - 3.
0-3
0 -3/5
O 1/5
05

The apothem of the hexagon is 8√3 cm.

We are given that;

The area of a regular hexagon= 384√3Cm²

Now,

To find the side length, radius, and apothem of a regular hexagon given its area, we can use the following formulas:

Area = (3√3 s^2) / 2 Area = (1/2) a P Area = (3/2) r a

where s is the side length, a is the apothem, P is the perimeter, and r is the radius of the hexagon. We can solve for any of these variables by rearranging the formulas and plugging in the given area.

A. To find the side length, we can use the first formula and solve for s:

s^2 = (2 Area) / (3√3) s = sqrt((2 Area) / (3√3))

Plugging in Area = 384√3, we get:

s = sqrt((2 * 384√3) / (3√3)) s = sqrt(256) s = 16

Therefore, the side length of the hexagon is 16 cm.

B. To find the radius, we can use any of the formulas and solve for r. For example, using the third formula, we get:

r = (2 Area) / (3 a)

To find a, we can use the second formula and solve for a:

a = (2 Area) / P

To find P, we can use the fact that P = 6s and plug in s = 16:

P = 6 * 16 P = 96

Plugging in P and Area into the formula for a, we get:

a = (2 * 384√3) / 96 a = 8√3

Plugging in a and Area into the formula for r, we get:

r = (2 * 384√3) / (3 * 8√3) r = 32

Therefore, the radius of the hexagon is 32 cm.

C. To find the apothem, we can use any of the formulas and solve for a. For example, using the second formula, we get;

a = (2 Area) / P

Plugging in Area = 384√3 and P = 96, we get:

a = (2 * 384√3) / 96 a = 8√3

Therefore, by polygon the answer will be 8√3 cm.

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Required two transformations are translated according to the rule (x, y) → (x + 8, y + 2) reflected across the x-axis.

How to find the two transformations applied to pentagon ABCDE to create A″B″C″D″E″?

To find the two transformations applied to pentagon ABCDE to create A″B″C″D″E″, we can compare the coordinates of corresponding vertices of both pentagons.

Starting with point A, we see that it has been translated 8 units to the right and 2 units up to become A″. Therefore, the first transformation is a translation according to the rule (x, y) → (x + 8, y + 2).

Next, we can compare the y-coordinates of point A and A″ to see if a reflection has been applied. We see that the y-coordinate of A has changed from 5 to -7 in A″, indicating that a reflection has been applied across the x-axis.

Therefore, the two transformations applied to pentagon ABCDE to create A″B″C″D″E″ are:

Translated according to the rule (x, y) → (x + 8, y + 2)

Reflected across the x-axis.

The other options can be ruled out as they do not correctly reflect the transformation that was applied.

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Check the picture below.

so the parabolic path of the object is more or less like the one shown below in the picture, now this object has an initial of 1240 ft, as it gets thrown from the ski lift, so from 0 seconds is already higher than 1000 feet.

\(h=-16t^2+32t+1240\hspace{5em}\stackrel{\textit{a height of 1000 ft}}{1000=-16t^2+32t+1240} \\\\\\ 0=-16t^2+32t+240\implies 16t^2-32t-240=0\implies 16(t^2-2t-15)=0 \\\\\\ t^2-2t-15=0\implies (t-5)(t+3)=0\implies t= \begin{cases} ~~ 5 ~~ \textit{\LARGE \checkmark}\\ -3 ~~ \bigotimes \end{cases}\)

now, since the seconds can't be negative, thus the negative valid answer in this case is not applicable, so we can't use it.

So the object on its way down at some point it hit 1000 ft of height and then kept on going down, and when it was above those 1000 ft mark  happened between 0 and 5 seconds.

The probability that exactly one box remains empty = 9/16

Let us assume that b₁, b₂, b₃ and b₄ be four distinct balls and M₁, M₂, M₃ and M₄ are four boxes.

The total number of ways in which 4 different balls b₁, b₂, b₃ and b₄ can be placed in 4 distinct boxes would be,

n = 4⁴

And the number of ways to choose an empty box = ⁴C₁

The four balls must be distributed to the remaining 3 boxes so that no box is left empty. This means means one of those three boxes will receive two balls and the others will each receive one. There are ³C₁ ways to choose the box that will receive two balls and ⁴C₂  ways to choose which two balls will be placed in that box. The remaining balls can be placed in the remaining two boxes in 2! ways.

So, the number of ways that exactly one box remains empty

= ⁴C₁ × ³C₁ × ⁴C₂ × 2!

= 144

so, the required probability would be,

P = 144/ 4⁴

P = 9/16

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The simulation of the virtual dice roller illustrates combination and sample space

There are 36 different ways you can dress every morning

The sample space of the two dice are:

Die 1 = {1,2,3,4,5,6}

Die 2 = {1,2,3,4,5,6}

From the above sample space, we have the sample size to be:

n(Die 1) = 6

n(Die 2) = 6

The sample size of the experiment would be:

n = n(Die 1) * n(Die 1)

Substitute known values

n = 6 * 6

Evaluate the product

n = 36

The above represents the different ways you can dress every morning.

Hence, there are 36 different ways you can dress every morning

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Answer:

Step-by-step explanation:

sin (B) = \(\frac{2}{5}\)

a) Comparing the two functions, Scooter's business has a lower slope of 15 compared to Karissa's business with a slope of 35. b) Both Scooter and Karissa earned a total of $500 in that month. Therefore, they had an equal month in terms of total money earned.

a) In the context of Scooter's business, the slope of the function f(x) = 200 + 15x represents the rate at which the total money earned increases with each additional sale. Each unit increase in x (number of sales) results in an increase of $15 in total money earned. The y-intercept of 200 represents the initial amount of money Scooter already had before making any sales.

In the context of Karissa's business, the slope of the function f(x) = 80 + 35x represents the rate at which the total money earned increases with each additional repair job. Each unit increase in x (number of repairs) results in an increase of $35 in total money earned. The y-intercept of 80 represents the initial amount of money Karissa already had before doing any repair jobs.

Comparing the two functions, Scooter's business has a lower slope of 15 compared to Karissa's business with a slope of 35. This means that Karissa's business earns more money per repair job compared to Scooter's business per t-shirt sale.

b) To determine who had the better month, we need to calculate the total money earned by each individual based on the given sales/repairs.

For Scooter, with x = 20 (number of shirts sold):

f(x) = 200 + 15x

f(20) = 200 + 15 * 20

f(20) = 200 + 300

f(20) = 500

For Karissa, with x = 12 (number of repairs):

f(x) = 80 + 35x

f(12) = 80 + 35 * 12

f(12) = 80 + 420

f(12) = 500

Both Scooter and Karissa earned a total of $500 in that month. Therefore, they had an equal month in terms of total money earned.

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The statement that correctly written as a conditional statement is; A number, such as 10, is a composite number because it is even. so the correct option is D.

Natural numbers are: 1, 2, 3, ....

Integer numbers are: ...., -2, -1, 0, 1, 2, ... (so it includes positive and negative natural number, and 0 )

Rational numbers are numbers which can be written in the form of a/b  

where a and b are integers.

Irrational numbers are those real numbers which are not rational numbers.

Here, Know that all natural numbers are integers, all integers are rational numbers. That means, natural numbers are not irrational.

A composite number is a number divisible by another number than 1 and the number itself.

To find example, a sum of two composite numbers, which is not a composite number, is needed.

The statement that correctly written as a conditional statement is; A number, such as 10, is a composite number because it is even.

Hence so the correct option is D.

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Answer:

the answer will be 4/36

Answer:

10.00

Step-by-step explanation:

because 2.00 x 5 is 10 which is a hundred percent hope this helps!

Transformation is the process of changing one form or structure into another. Here are some key points about transformation:

• Physical transformations involve changing the physical properties of an object, like shape, size, state of matter, etc. Some examples are cutting, bending, melting, freezing, dissolving, combining substances, etc.

• Chemical transformations involve changing the chemical composition of a substance, forming new substances with different properties. Some examples are chemical reactions that produce new compounds, oxidation reactions, decomposition, synthesis reactions, etc.

• Biological transformations occur within living organisms through processes like development, growth, metabolism, adaptation, and evolution. These changes occur over time and at the cellular or molecular level.

• Mathematical transformations involve applying operations or functions to mathematical objects like numbers, vectors, matrices, etc. to produce new outputs. Common transformations include translation, rotation, reflection, scaling, and projection.

• Information transformations occur when data is manipulated, organized, or changed. Examples are data compression, encryption, encoding, classification, and filtering of information.

• Conceptual transformations refer to changes in a person's knowledge, understanding, perspectives, beliefs, attitudes, or behavior. Things like experiences, education, and realizations can cause conceptual transformations.

The key aspects of any transformation are that there is an initial state or form that undergoes some change process resulting in an altered final state or form. There are often changes to properties, composition, structure, or relationships involved.

Hope this explanation of transformation helps! Let me know if you have any other questions.

Transformation can refer to a marked change in form, nature, or appearance. It can also refer to a process by which one figure, expression, or function is converted into another one of similar value.

Answer:

k ≤ 8 or k ≥ 32/3

I'm not 100% sure on this so feel free to correct me if im wrong.

Answer:

k=≤-8 or k≥\(\frac{32}{3}\)

Step-by-step explanation:

The customer gets 5.66 hours of bike per dollar

At Hoffman's bike, it cost $17 to rent a bike for 3 hours

The number of hours gotten from the bike per dollar can be calculated as follows

17= 3
1= x

Cross multiply both sides

3x= 17

x= 17/3

x= 5.66

Hence it will cost the customer 5.66 hours to rent the bike for one dollar

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Let:

y = Total cost

x = Number of attendees

b = Flat fee = 104

a = Cost of books = $18

c = Payment of each attendee = $26

The cost function will be given by:

The revenue function will be:

In order to the company will be breaking even:

Solve for x:

It will take 13 attendees and the company's total expenses and revenues at that point is:

$338

Answer:

13 attendees and $338

Answer: Option C = 5x^2 + 12x - 7

Step-by-step explanation: First, we need to combine like terms.

-2x^2 + 8x - 9 + 4x + 7x^2 + 2 = (7x^2 - 2x^2) + (4x + 8x) + (-9 + 2) = 5x^2 + 12x - 7

So the expression is equivalent to option C, which is 5x^2 + 12x - 7.

Answer:

ITS THE FIRST ONE

Step-by-step explanation:

-2X2+8

HOPE THIS HELPS

Answer:

33232.92

Step-by-step explanation:

The number of each kite the manufacturer can produce to maximize profit are;

90 standard kites or 64 deluxe kites

Profit maximization is a process used to increase the profit of a company to the highest levels.

Let x represent the number of standard kite produced and let y represent the number of deluxe kite produced. Let p represent the profit from selling one standard kite and let q represent the profit from selling one deluxe kite.

The constraints inequalities that can be obtained to solve the question using linear programming methodology are therefore;

2·x + 3·y ≤ 200 (The fabric constraints)

5·x + 7·y ≤ 450 (The string constraints)

x ≥ 0, y ≥ 0 (Non–negative constraints)

The objective function which is the total profit can be presented as follows;

z = p·x + q·y (total profit)

Therefore, we get;

Maximize: z = p·x + q·y

Subject to:

2·x + 3·y ≤ 200

5·x + 7·y ≤ 450

x ≥ 0, y ≥ 0

The graph of the above inequalities indicates that we get the following coordinates of the vertices of the feasible region;

(0, 64 2/7), (90, 0), (0, 0)

The objective function indicates that we get;

z(0, 64 2/7) = p × 0 + q × 64 2/7 = (64 2/7)·q

z(90, 0) = p × 90 + q × 0 = p × 90 = 90·p

z(0, 0) = p × 0 + q × 0 = 0

The company can produce 90 standard kites or 64 deluxe kites to maximize their profit

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Answer:

FH = 35.64

Step-by-step explanation:

(∠A = 360 so the other angle is 40)

By law of cosines,

FH² = AH² + FA² - 2(AH)(FA) * cos(A)

= 30² + 25² - 2(30)(25) * cos(80)

= 900 + 625 - 1500 * 0.17

= 1525 - 255

FH²  = 1270

FH = √1270

FH = 35.64

-1

We can solve in this way,

-3x-5x+8=16

-8x=16-8

-8x=8

x= -8/8

x= -1

Therefore for this equation, x= -1.

Answer:

Elon Musk 269.7 B
Jeff Bezos: 170.15 B
Bill Gates: 130.23 B

Step-by-step explanation:

If you had a trail of 1 billion 1 dollar bills, it would stretch out to 96,900 miles.

If you did that with 100 billion 1 dollar bills, that would be 9,690,000 miles.

That is more than 300 times the circumference of the Earth.

Answer:

unfortunately i cannot tell you the exact answers; however, i can suggest something instead. my suggestion is that if there's any math notes that are available, maybe you could look over them-then apply that to the problems.

Step-by-step explanation:

I hope this helps you!

The class that had better overall results on the exam is class A.

The class with greater variability in results is class B.

The statistics of students in class A:

\(\text{Maximum score} = 100\)

\(\text{Minimum score} = 65\)

\(\text{Median} = 85\)

\(\text{First quartile}=\dfrac{1}{4} (n + 1) = \dfrac{1}{4} \times 12= 3\text{rd} \ \text{term} = 70\)  

\(\text{Third quartile} =\dfrac{3}{4} \times (n + 1) = \dfrac{3}{4} \times 12= 9\text{th} \ \text{term} = 90\)

The statistics of students in class B:

\(\text{Maximum score} = 100\)

\(\text{Minimum score} = 55\)

\(\text{Median} = 75\)

\(\text{First quartile} = 70\)

\(\text{Third quartile} = 80\)

The range would be used to determine which class has greater variability.

\(\bold{Range} = \text{highest score - lowest score}\)

\(\bold{Class \ A} = 100 - 65 = 35\)

\(\bold{Class \ B} = 100 - 55 = 45\)

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Answer:

she can buy 3

Step-by-step explanation: 3.50x3=10.50 which is the closest you can get without going over the price range

Step-by-step explanation:

I assume AB is supposed to be a straight line. yes ?

in that case please remember that all angles on top of a line (and then again below a line) must sum up to 180 degrees (this is what it takes to flip a "stick" on that line from left to right).

so, COD covers already 90 degrees of these 180.

that means AOD + BOC = 180 - 90 = 90 degrees.

now we know that the 2 angles are in the ratio of 1:5.

that means that BOC is 5 times as large as AOD.

and we can be more direct :

since the 2 angles are in the ratio 1:5 we are actually splitting the remaining 90 degrees into 6 parts (5+1).

and BOC gets then 5 of these 6 parts, and AOD gets the remaining 1 part.

so,

90/6 = 15

therefore, one of these parts is 15 degrees.

so, we know AOD = 15 degrees.

BOC = 5×15 = 75 degrees

or simply 90 - 15 = 75 degrees

Answer:

Step-by-step explanation:

7 - 3 = 4 so 4

my tiger drawing is cool

Lee's TV costs $4.05 to operate for a month of 30 days.

To calculate the cost of operating Lee's TV for a month, we need to find out the total number of kilowatt-hours (kWh) of electricity consumed by the TV during that time.

First, let's find out how many watts Lee's TV consumes in a day:

250 watts/hour x 3 hours/day = 750 watts/day

To convert this to kilowatts, we divide by 1000:

750 watts/day ÷ 1000 = 0.75 kilowatts/day

Now, we can calculate the total number of kilowatt-hours consumed by the TV in a month:

0.75 kilowatts/day x 30 days = 22.5 kilowatt-hours

Finally, we can calculate the cost of operating the TV for a month:

22.5 kilowatt-hours x 18 cents/kilowatt-hour = $4.05

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The term that can be added to the list so that the greatest common factor of the three terms  12h3 36h3, 12h6, is 48h5

A group of numbers' greatest common factor (GCF) is the biggest factor that all the numbers have in common. For instance, 12, 20, and 24 all share two characteristics.

The term that  can fit in to the list so the GCF is 12h3 would be 48h5, this is so because 48 is first divisible by 12  without any  fraction, and we can remove upon dividing 3 h's from this term as it contains a total of 5 h's.

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