1. Find the Area of the Sector:


2. Find the length of the missing side:

1. Find The Area Of The Sector:2. Find The Length Of The Missing Side:
1. Find The Area Of The Sector:2. Find The Length Of The Missing Side:

Answers

Answer 1
Answer:

1. Area of sector is 14.14 sq.m

2. Length of the missing side is 10 cm

Step-by-step explanation:1.)

Using formula:

Area of sector = θ/360° × π r²

Where,

θ = 45° Radius (r) = 6m

Substituting the required values:

→ Area = 45°/360° × 22/7 × (6)²

→ Area = 0.125 × 22 × 36/7

→ Area = 2.75 × 36/7

→ Area = 99/7

→ Area = 14.14 sq.m

2.)

In given right angled traingle:

Perpendicular = 6 cmBase = 8 cmHypotenuse = ?

Using Pythagoras theorem,

(H)² = (B)² + (P)²

where,

H is hypotenuseB is Base P is perpendicular

Substituting the required values:

→ (Hypotenuse)² = (8)² + (6)²

→ (Hypotenuse)² = 64 + 36

→ (Hypotenuse)² = 100

→ Hypotenuse = √100

→ Hypotenuse = 10 cm

Hence,

Hypotenuse of Traingle is 10 cm

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red and green

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A linear function has a y-intercept of 3 and passes through the point (3, 7). Tom compared the slope of the function to the slope of 4x - y = 5. What is the difference in the two slopes?

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 y = 4x² + 24x + 38

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Answer: 6. this is like 3rd grade math just multiply 1/3 and 1/6 to see

Answer:

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Step-by-step explanation:

1/6/1/3=1/2or2

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X + Y-2 (3X-4Y+3) please simplify this
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Answers

Answer:

-5x+9y-6

Step-by-step explanation:

Step 1:

Remove bracket,  

x+y-6x+8y-6

collect like terms and simplify,

x-6x+y+8y-6= -5x+9y-6

Find the volume of the cone. Round your answer to the nearest tenth.

Answers

[tex]\qquad\qquad\huge\underline{{\sf Answer}}♨[/tex]

Let's solve ~

Radius (r) = 2 cm

height (h) = 8 cm

Now, let's apply the formula :

[tex]\qquad \sf  \dashrightarrow \:v = \frac{1}{3} \pi {r}^{2} h[/tex]

[tex]\qquad \sf  \dashrightarrow \:v = \frac{1}{3} \times 3.14 \times {(2)}^{2} \times 8[/tex]

[tex]\qquad \sf  \dashrightarrow \:v = \frac{100.48}{ 3} [/tex]

[tex]\qquad \sf  \dashrightarrow \:v = 33.49333333.....[/tex]

[tex]\qquad \sf  \dashrightarrow \:v \approx33.5 \: \: cm {}^{3} [/tex]

Given that lines b and c are parallel, select all that apply.

Which pairs of angles are congruent?

3 and 7
2 and 8
3 and 5
1 and 4

Answers

Answer:

3 and 7

1 and 4

Step-by-step explanation:

[3 and 7]

These two angles are prooved congruent by corresponding angles

[1 and 4]

These two angles are prooved congruent by opposite vertical angles.

1. a) Solve the following linear-quadratic system of equations graphically.
y + 2x²– 8x – 1= 0
y+ 2x – 9= 0

b.) GRAPH

c.) Verify your solution (s) algebraically.

Answers

Answer:

please see explanation

Step-by-step explanation:

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Twelve people apply for a teaching position in mathematics at a local college. Six have a PhD and six have a master’s degree. If the department chairperson selects three applicants at random for an interview, find the probability that all three have a PhD

Answers

Using the hypergeometic distribution, it is found that there is a 0.0175 = 1.75% probability that all three have a PhD.

The applicants are chosen without replacement, hence the hypergeometric distribution is used to solve this question.

What is the hypergeometric distribution formula?

The formula is:

[tex]P(X = x) = h(x,N,n,k) = \frac{C_{k,x}C_{N-k,n-x}}{C_{N,n}}[/tex]

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

The parameters are:

x is the number of successes.N is the size of the population.n is the size of the sample.k is the total number of desired outcomes.

In this problem, the values of the parameters are as follows: N = 20, k = 6, n = 3.

The probability that all three have a PhD is P(X = 3), hence:

[tex]P(X = x) = h(x,N,n,k) = \frac{C_{k,x}C_{N-k,n-x}}{C_{N,n}}[/tex]

[tex]P(X = 3) = h(3,20,3,6) = \frac{C_{6,3}C_{14,0}}{C_{20,3}} = 0.0175[/tex]

0.0175 = 1.75% probability that all three have a PhD.

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Factor completely 2x2 − 2x − 40. 2(x − 5)(x 4) (2x − 10)(x 4) (x − 5)(2x 8) 2(x − 4)(x 5).

Answers

The factor the given polynomial are 2,(x+4),(x-5).

We have given that the equation,

[tex]2x^2 -2x -40[/tex]

What is the meaning factor?

Factoring a polynomial is expressing the polynomial as a product of two or more factors.

We can factor out a 2.

[tex]2(x^2 - x - 20)[/tex]

Now, we can write down the 2 and factor the [tex](x^2 - x - 20)[/tex].

[tex](x^2-x - 20)=x^2-5x+4x-20\\ =x(x-5)+4(x-5)\\ =(x+4)(x-5)[/tex]

[tex]f(x)=2x^2 -2x -40=2(x^2 - x - 20)=2(x+4)(x-5)[/tex]

Therefore, the factor the given polynomial are 2,(x+4),(x-5).

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Hyperbolas are confusingggg

A skateboard halfpipe is being designed for a competition. The halfpipe will be in the shape of a parabola and will be positioned above the ground such that its focus is 30 ft above the ground. Using the ground as the x-axis, where should the base of the halfpipe be positioned? Which equation best describes the equation of the halfpipe?

(0, 60); y equals one over two hundred forty times x squared minus 60
(0, 60); y equals one over two hundred forty times x squared plus 60
(0, 15); y equals one over sixty times x square minus 15
(0, 15); y equals one over sixty times x squared plus 15

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Answer:

I think the answer is A but im not sure

Approximately how many grams of radium will remain after 4 grams have decayed for 2400 years

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Answer:

1.4

Step-by-step explanation:

In what year did the nfl vote to create a $430 million pool of money, funded by the top 15 clubs by revenue to be distributed to the bottom 15 clubs?.

Answers

The year in which the NFL voted to create a $430 million fund to help the bottom 15 clubs was 2007.

When did the NFL vote to implement this fund?

The NFL voted by a margin of 30-2 in 2007 to create a pool of funds over 3 years that would amount to $430 million.

This money would then be used to help the bottom 15 clubs who might be struggling financially. The hope was that this would make things more competitive in the NFL.

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This composite figure is created by placing a sector of a circle on a rectangle. What is the area of this composite figure? Show your work.

Answers

Answer:

area of the figure: 29.92 m²

formula's:

area of rectangle: length * widtharea of sector: ∅/360 * πr²

solving steps:

area of rectangle + area of sector

5.5 * 4 + 30/360 * π(5.5)²

22 + 7.919

29.92 m²

Answer:

Calculate the area of the sector and the area of the rectangle separately, then add them together to determine the area of the composite figure.

Rectangle

Area of a rectangle = width × length

                                = 4 × 5.5

                                = 22 m²

Sector

[tex]\textsf{area of sector}=\dfrac{\theta\pi r^2}{360} \textsf{ (when } \theta \textsf{ is measured in degrees)}[/tex]

                     [tex]=\dfrac{30 \cdot\pi\cdot5.5^2}{360}[/tex]

                     [tex]=\dfrac{121}{48}\pi \textsf{ m}^2[/tex]

Total area

total area = area of rectangle + area of sector

                [tex]=22 +\dfrac{121}{48}\pi[/tex]

                = 29.91943148...

                = 29.9 m² (nearest tenth)

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Answers

Answer:

Domain: (-∞, -5) ∪ (-1, ∞)

Step-by-step explanation:

Note:

For f(x) > 0: See the points of x for which the graph of f(x) lies above the x-axis.

For f(x) < 0: See the points of x for which the graph of f(x) lies below the x-axis.

We need to find the domain of f(x) for which f(x) < 0

From the graph, we can tell:

f(x) < 0 on (-∞, -5) ∪ (-1, ∞)

Therefore: The domain on which the given graph f(x) is negative, is (-∞, -5) ∪ (-1, ∞)

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Answers

Answer:

LAST CHOICE IS THE ANSWER.

Step-by-step explanation:

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Answer:

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Step-by-step explanation:

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tan (θ) = [tex]-\sqrt{3}[/tex]

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Answers

Answer:

k = 12h

Step-by-step explanation:

Since each of the inputs of h can be mutiplied by 12 to get the output k, the equation is k = 12h
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Stretch
2. A gym runs two fitness classes, spinning and circuits.
On Saturday 100 people visited the gym.
18 people attended the spinning class.
10 people attended both classes.
56 people did not attend either class.
a) Represent this information on a Venn diagram

S
Ic с
10
(3)
56
A person who attended the gym is selected at random. .
Find the probability that this person:
b) attended only circuits
(2)
c) attended exactly one class
(2)
d) attended spinning, given that they attended circuits
. (2)

Answers

The probability that a person chosen at random attended only circuits is 0.16.

The probability that a person chosen at random attended  exactly one class is 0.0288.

The probability that a person chosen at random attended spinning, given that they attended circuits is 0.10

What is the probability?

Probability determines the chances that an event would happen. The probability the event occurs is 1 and the probability that the event does not occur is 0.

Probability a person chosen at random attended only circuits = number of people who atended circuits / total number of the people at the gym

16/100 = 0.16

Probability a person chosen at random attended exactly one class  = (number of people who atended circuits only / total number of the people at the gym) x (number of people who atended spinning class only / total number of the people at the gym)

16/100 x 18/100 = 0.0288

Probability a person chosen at random attended  spinning, given that they attended circuits= 10/100  = 0.10

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Answers

Answer: (x−6)(x−1)(x+1)

Use the graphing calculator to graph the quadratic function y = x2 − 5x − 36. Which value is a solution of 0 = x2 − 5x − 36?

−9
−4
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6

Answers

Answer: -4

Step-by-step explanation:

Once you graph it, the solutions are where the graph meets the x axis.

This is at -4 and 9.

A pair of fair dice is cast. What is the probabiliy that one of the numbers falling uppermost is a 5, given that the two numbers falling uppermost are different?.

Answers

Using it's concept, it is found that there is a 0.3333 = 33.33% probability that one of the numbers falling uppermost is a 5.

What is a probability?

A probability is given by the number of desired outcomes divided by the number of total outcomes.

The outcomes are given as follows:

(1,1), (1,2), (1,3), (1,4), (1,5), (1,6)

(2,1), (2,2), (2,3), (2,4), (2,5), (2,6)

(3,1), (3,2), (3,3), (3,4), (3,5), (3,6)

(4,1), (4,2), (4,3), (4,4), (4,5), (4,6)

(5,1), (5,2), (5,3), (5,4), (5,5), (5,6)

(6,1), (6,2), (6,3), (6,4), (6,5), (6,6)

From the list, we have that:

There are 30 outcomes in which the numbers are different.In those, there are 10 in which one 5 appears.

Hence, the probability is given by:

p = 10/30 = 0.3333 = 33.33%.

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if 2.5kg of potatoes cost £1.40
work out the cost of 4.25kg of potatoes

Answers

Answer:2.5 kg of potatoes cost £1.40 Work out the cost of 4.25 kg of potatoes. 1.25kg=70p 2.5 kg=1.40 3.75 kg=2.10 Done.

Step-by-step explanation: hope this helps love!!

PLEASE HELP A.S.A.P.!

Solve the equation:

|x-1|+|x-2|=3

Answers

X=3

Explanation-

(x-1)+(x-2)=3
x-1+(x-2)=3
x-1+x-2=3
Then collect the two like terms
x-1+x-2=3=
2x-1-2=3
Calculate the difference
x-1+x-2=3=
2x-3=3
———————
2x-3=3
Move the constant to the right-hand side and change its sign
2x=3+3
———————————————————-
2x=3+3
Add the numbers

2x=6
————————————————-
2x=6

Divide both sides of the equation by two

X=3

There you go. Have a great day! :)

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find the area of the circles ​

Answers

10) 655785 cm 11) 706 cm 12) 1962 cm

Answer:

10) 25π OR 78.5398...yd 11) 1/4π OR 0.785398...ft 12) 100π OR 314.159265....in

Step-by-step explanation:

area of a circle = πr^2 (π x radius squared)
the radius is just half the diameter

so for eg:

number 10)

diameter = 10 yd so radius = 5 yd

5 squared = 25

π x 25 yd = 25π OR 78.5398...yd

i hope this helped :)

Bobby's cat runs x mph. Bobby's dog runs twice as fast as his cat.
If cat and dog start running away from each other how far away from each other will they be after 30 minutes?

Answers

The distance they(Bobby's cat and dog) will be from each other after 30 minutes is 0.5x miles.

Calculation of distance

The dog runs twice as fast as the cat. Therefore,

Bobby's cat speed = x

Bobby's dog speed = 2x

Therefore,

speed  = distance / time

30 minutes = 0.5 hours

Therefore,

distance = speed × time

distance covered by the cat = x × 0.5 = 0.5x

distance covered by the dog = 2x × 0.5 = x

Therefore, the distance they will be from each other after 30 minutes is as follows:

distance = x - 0.5x = 0.5x

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A kite string is 100 feet long from the kite to the ground. The string makes a 45° angle with the ground
About how high off the ground is the kite? Leave your answer as a simplified radical

Answers

Answer:

It's not very high

Step-by-step explanation:

The angle that the string and the ground maje, is acute, because it's smaller than a right angle. So, since it is an acute angle, it's not very high. It is about 30cm high.

How much, in total, did Noel spend to cash her three most recent paychecks?

Answers

The total amount of money that was spent by Noel to cash her three (3) most recent paychecks is equal to $10.99.

What is a paycheck?

A paycheck can be defined as a financial document that is issued by an employer to an employee as payment for the work done over a period of time.

How to calculate the amount spent.

From the table, we can see that the amount of money charged by the bank as check processing fee is equal to $1.99, as well as 1.99% (0.0199) of the amount being cashed by a customer.

Thus, we would compute the amount of money spent by Noel as follows:

Noel = (0.0199 × 100.53) + (0.0199 × 119.38) + (0.0199 × 122.52) + (1.39 × 3)

Noel = 2.00 + 2.38 + 2.44 + 4.17

Noel = $10.99.

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·[tex]3\sqrt{10}\ times -6\sqrt{30}[/tex]

Due by 12:23

Answers

Answer:

-180√3

Step-by-step explanation:

3√10 x - 6√30

= 3x-6 x -√10 x √30

= -18 x√300

= -18 x 10√3

= -180√3

Please help! will give brainlest! locks in 30 min!

Answers

Answer:

[tex]\frac{\sqrt{2} }{2}[/tex]

Step-by-step explanation:

Simplify the expression:

sin [tex]\frac{3pi}{4}[/tex]

Rewrite the angle as a sum or difference with its reference angle:

sin (pi - [tex]\frac{pi}{4}[/tex])

Simplify the expression

(sin [tex]\frac{pi}{4}[/tex])

Evaluate the expression:

[tex]\frac{\sqrt{2} }{2}[/tex]

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