a sector with a radius of 12cm has an area of 60pi cm what is the central angle in radians​

Answer:

2

Step-by-step explanation:

substitute n=1 and n=3 in the given equation

1 st term is (1)^2-1-2 = 1 -1 -2 = -2

3rd term is (3)^2-3-2 = 9-3-2=4

sum of 1st and 3rd term is -2 + 4 = 2

Answer:

  £531.52

Step-by-step explanation:

We are given the profit in week 1 and information about week 2. We are asked for the difference between week 2 profit and week 1 profit.

__

In week 2, pizza is sold 4 ways. The diagram shows the numbers of pizzas sold each way. The table shows the profit made for each way the pizza was sold. We need to add up the profits from each of the sales to find the profit for week 2.

Then the total profit in week 2 is ...

  £1514.04 -175.42 +888.94 -5.68 = £2221.88

So, profit in week 2 exceeds profit in week 1 by ...

  £2221.88 -1690.36 = £531.52 . . . more profit in week 2

Answer:

The difference between the two throws is 6/7 yards

Step-by-step explanation:

Beatrice throw=1 7/14 yards

Tilly throw=9/14 yards

Difference between the two throws=Beatrice throw - Tilly throw

=1 7/14 - 9/14

=21/14 - 9/14

= 21-9/14

=12/14

=6/7 yards

The difference between the two throws is 6/7 yards

Answer:

A. Choosing the third person listed on every fifth page of the phone book is stratified sampling.

Step-by-step explanation:

Stratified sampling involves grouping the population into subgroups before sampling. It provides a more manageable and cheaper means of sampling data by placing the population into grouped strata. The only problem is that this sampling method cannot be used in a data population that cannot be stratified. In this question, the phone book is stratified into subgroups of every five pages, and the third person listed is chosen to represent the subgroup

Answer:

2 by 3

Step-by-step explanation:

please mark brainliest if it helped

Answer:

8 ft

Step-by-step explanation:

We can use ratios to solve

tree                          Otis

--------------------  = --------------

tree shadow          Otis shadow

tree                   4 ft

-------------- = ----------------

9 ft                   4.5 ft

Using cross products

4.5 tree = 4* 9

4.5 tree = 36

Divide each side by 4.5

tree = 36/4.5

tree =8

Answer:

8.1

Step-by-step explanation:

Answer:

There is no relationship, except they do intersect at the point (1, -1). Hope this helps :)

Brainliest?

Both given lines are going to intersect at ( 1,-1 ) that's it.

A line section that can connect two places is referred to as a segment.

The line is here! It extends endlessly in both directions and has no beginning or conclusion.

In other words, a line segment is just part of a big line that is straight and going unlimited in both directions.

Given that

Line 1 ; 5x +y = 4

Line 2 ;  20 + 4y = 16 ⇒ y = -1

At  y = -1  the first line is

5x  - 1  =  4 ⇒ x = 1

So,

It is clear that line 1 has a point ( 1 .-1 ) and line 2 also passes

through it hence there will an intersection.

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Answer:

544 cups

Step-by-step explanation:

1 gallon consists of about 16.0047 cups, 34x16 is 544

Answer:

Option (A)

Step-by-step explanation:

By satisfying the equation of a function 'f' by each coordinates given in the options we can get the point which lies on the graph of f(x) = [tex]2\times (5)^x[/tex]

Option (A). (1, 10)

f(1) = [tex]2\times (5)^1[/tex]

10 = 10

True.

Therefore, point (1, 10) lies on the graph.

Option (B). (0, 10)

f(0) = [tex]2\times 5^0[/tex]

10 = 2

Not true.

Therefore, point (0, 10) doesn't lie on the graph.

Option (C). (10, 1)

f(10) = [tex]2\times 5^{10}[/tex]

1 = 19531250

Not true.

Therefore, point (10, 1) doesn't lie on the graph.

Option (D). (0, 0)

f(0) = [tex]2\times 5^0[/tex]

0 = 2

Not True.

Point (0, 0) doesn't lie on the graph.

Option (A) will be the answer.

Answer:

33

Step-by-step explanation:

15019 / 53 = 283 R20

53 − 20 = 33

He needs 33 more trees so that every row can have the same number of trees.

Answer:

Is this what you are looking for....

Answer:

x=±√3 or ±1.732

Step-by-step explanation:

5x²-9=6

5x²=6+9

5x²=15

x=±√15/5

x=±√3

Answer:

x=-7  x=4

Step-by-step explanation:

(X-2)(x+5)=18

FOIL

x^2 +5x -2x-10 =18

Combine like terms

x^2 +3x -10 = 18

Subtract 18 from each side

x^2 +3x -10 -18 = 0

Combine like terms

x^2 +3x -28 =0

Factor

What two numbers multiply to -28 and add to 3

7*-4 = -28

7+-4 = 3

( x+7) ( x-4) =0

Using the zero product property

x+7 =0  x-4=0

x=-7  x=4

Answer:

y + c ÷ m = x

Step-by-step explanation:

You start of with:

y = mx - c

We can get rid of the + c by putting it on the other side. When a number goes to the other side it does the opposite, so the - will become a +. It will end up as:

y + c = mx

We just need x on itself so we need to get ride of m. In this sum, mx means that they are multiplying together, we need to make that divide. So we take m on the other side and make it divide. This brings us to x on itself.

(y+c) ÷ m = x

Hope this helps.

x can be changed into the subject of the formula as x = (y + c) / m.

An equation is the statement of two expressions located on two sides connected with an equal to sign. The two sides of an equation is usually called as left hand side and right hand side.

Subject of an equation is that variable we are going to find out.

The given equation is y = mx - c.

Here y is the subject.

We need to rewrite the equation to make x the subject.

y = mx - c

Adding c on both sides,

y + c = mx - c + c

y + c = mx

Dividing both sides by m, we get,

(y + c) / m = mx / m

(y + c) / m = x

Hence the given formula y = mx - c can be rewritten to make x the subject as x = (y + c) / m.

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Hey there! I’m happy to help!

Let’s first subtract 4 from 20 to see how much was lost.

20-4=16

Now, we see that 16 is a certain percent of twenty that we want to find. When talking about percents, the word “is” represents an equal sign. So, we can write this equation. We will have p represent our prevent.

16=20p (16 is a certain percent of 20)

Now, we solve by dividing both sides of the equation by 20 to isolate the p.

p=0.8

0.8 is 80% or 4/5, so 4/5 of the dam water has been lost.

Have a wonderful day! :D

Answer:

Pretty simple!

Step-by-step explanation:

First, you need to know about exponential functions. They are like linear functions, but either increase or decrease their rate as they go further along the x-axis.

Linear functions take a simple form: Just a line. Not really much to it!

Their equation is: [tex]y=mx+b[/tex]

Yeah! Now onto Exponential Functions.

Exponential functions are very interesting. This could be that they are hard to solve sometimes, or that I spent over half a year studying them.

Their Graphs usually look like a line that keeps getting lower or higher as they progress.

Essentially, if they keep getting higher and higher(Y-axis wise), this means that they are increasing. Likewise, if they keep getting lower and lower, this means they are decreasing. Pretty simple, right?

Now, to state the slope over each part. To do that, I'm pretty sure you have to find two points that describe that area, use the formula for slope(Below), and I would think you are done.

[tex]m=\frac{y_{1} -y_{2} }{x_{1} -x_{2}}[/tex]

Hope this helps, and please correct me if I'm wrong!

Stay Safe!

Answer:

A=3244.8 dollars

Step-by-step explanation:

A=p(1+r)^t

A=3000(1+0.04)^2

A=3244.8 dollars

Answer:

a = 1, b = - 2

Step-by-step explanation:

The points that lie on the curve and straight line satisfy the corresponding equations.

Substitute the points into their corresponding equations, that is

(1, - 1 ) → - a = 1² + b = 1 + b ( multiply both sides by - 1 )

a = - 1 - b → (1)

(3, 3 ) → [tex]\frac{-3b}{2}[/tex] = [tex]\frac{3}{a}[/tex] ( cross- multiply )

- 3ab = 6 ( divide both sides by - 3 )

ab = - 2 → (2)

Substitute a = - 1 - b into (2)

(- 1 - b)b = - 2 , distribute left side

- b - b² = - 2 ( multiply through by - 1 )

b² + b = 2 ( subtract 2 from both sides )

b² + b - 2 = 0 ← in standard form

(b + 2)(b - 1) = 0 ← in factored form

Equate each factor to zero and solve for b

b + 2 = 0 ⇒ b = - 2

b - 1 = 0 ⇒ b = 1

Substitute these values into (1) for corresponding values of a

b = - 2 : a = - 1 - (- 2) = - 1 + 2 = 1

b = 1 : a = - 1 - 1 = - 2

Thus a = - 2, b = 1 or a = 1, b = - 2

Given that a > b then a = 1, b = - 2

Answer: probability of getting two 5s =0.04

probability of getting at least one 5 =0.36

probability of getting a total score greater than 5 =0.6

Step-by-step explanation:

Total outcomes on 1 spinner = 5

Then , total outcomes of spinning it 2 times=  [tex]5\times5 = 25[/tex]

Number of outcomes for getting two 5's = 1

Then, the probability of getting two 5s [tex]=\dfrac{\text{Favorable outcomes of getting two 5's }}{\text{Total outcomes}}[/tex]

[tex]=\dfrac{1}{25}=0.04[/tex]

Number of outcomes for getting at least one 5 [ {(1,5),(2,5),(3,5),(4,5),(5,5), (5,1), (5,2), (5,3), (5,4)} ] =9

Then, the probability of getting at least one 5[tex]=\dfrac{\text{Favorable outcomes of getting at least one 5 }}{\text{Total outcomes}}[/tex]

[tex]=\dfrac{9}{25}=0.36[/tex]

Number of outcomes for getting a total score of 5, [ {(1,4),(4,1),(2,3),(3,2)} ] =4

Then, the probability of getting a total score of 5,[tex]=\dfrac{\text{Favorable outcomes of getting a total score of 5 }}{\text{Total outcomes}}[/tex]

[tex]=\dfrac{4}{25}[/tex]

Number of outcomes for getting a total score greater than 5 [ {(1,5),(5,1),(2,4),(4,2),(2,5), (5,2), (3,4),(4,3), (3,5), (5,3), (3,3), (4,5), (5,4), (4,4), (5,5)} ] =15

Then, the probability of getting a total score greater than 5,[tex]=\dfrac{\text{Favorable outcomes of getting a total score greater than 5 }}{\text{Total outcomes}}[/tex]

[tex]=\dfrac{15}{25}=\dfrac{3}{5}=0.6[/tex]

Answer:

  two thirds, because the angles are complementary

Step-by-step explanation:

The cosine of an angle is equal to the sine of its complement.

  cos(23°) = 2/3 = sin(67°)

The cos23° = 2/3 = sin67° because the angles are complementary If the cos 23° = two thirds.

Trigonometry is a branch of mathematics that deals with the relationship between sides and angles of a right-angle triangle.

We have given:

cos23° = 2/3

The above expression can be written as:

cos(90-67) = sin67°    (cos(90-θ) = sinθ)

Thus, the cos23° = 2/3 = sin67° because the angles are complementary If the cos 23° = two thirds.

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Answer:

a. 0.6975

b. 0.25

c. The events are independent and inclusive

Step-by-step explanation:

a. The proportion of five-star football recruits in the nation that go to universities in the three most competitive athletic conferences = 75%

Therefore, the probability of a five-star football recruits chooses to go to a university in the three most competitive athletic conferences p(A) = 75% or 0.75

The proportion of the times five-star football recruits get full football scholarships = 93%

Therefore, the probability that a five-star football recruit get full football scholarships p(B) = 93% or 0.93

Therefore, the probability that a randomly selected five-star recruit who chooses one of the best three conferences will be offered a full football scholarship can be written as -the probability that a randomly selected five-star recruit who chooses one of the best three conferences and will be offered a full football scholarship is therefore;

p(A) ∩ p(B) = p(A) × p(B) = 0.75×0.93 = 0.6975

b. The probability that a randomly selected five star recruit will not select a university from one of the three best conferences = 1 - p(A) = 1 - 0.75 = 0.25

c. The events are independent as the given probability of occurrence of one event does not alter the probability of the other event

The events are inclusive events are exclusive events as P(A)and P(B) can take place simultaneously.

Hey There!!

Your correct choice will be C.

Step-by-step explanation:

Because, The cosine function is just the sine function translated 90° to the left, so it's a sinusoid. So, They named after the function sine. By ♡Itsbrazts♡

Answer:

Step-by-step explanation:

y=cos(x)-2

a. true

b. false ( angles should equal 180 125+65=190)

c. true

d. true

e. true

Answer:  19)  117°                    20) 53°

               21)  229°                   22) 119°

               23) 155°                    24) 323°

Step-by-step explanation:

Use Pythagorean Theorem to find r:     x² + y² = r²

19) x = [tex]-\sqrt{17}[/tex] ,  y = 8,    r = 9

     [tex]\cos \theta=\dfrac{x}{r} \rightarrow \quad \cos \theta =\dfrac{-\sqrt{17}}{9} \rightarrow \quad \theta = cos^{-1}\bigg(\dfrac{-\sqrt{17}}{9}\bigg)\rightarrow \quad \theta = \large\boxed{117^o}[/tex]

20) x = 3,   y = 4,   r = 5

      [tex]\cos \theta=\dfrac{x}{r} \rightarrow \quad \cos \theta =\dfrac{3}{5} \rightarrow \quad \theta = cos^{-1}\bigg(\dfrac{3}{5}\bigg)\rightarrow \quad \theta = \large\boxed{53^o}[/tex]

21) x = [tex]-\sqrt7[/tex],   y = -3,   r = 4

    [tex]\sin \theta=\dfrac{y}{r} \rightarrow \quad \sin \theta =\dfrac{-3}{4} \rightarrow \quad \theta = sin^{-1}\bigg(\dfrac{-3}{4}\bigg)\rightarrow \quad \theta = \large\boxed{229^o}[/tex]    

22) x = [tex]-\sqrt{15}[/tex],   y = 7,   r = 8

     [tex]\tan \theta=\dfrac{y}{x} \rightarrow \quad \tan \theta =\dfrac{7}{-\sqrt{15}} \rightarrow \quad \theta = tan^{-1}\bigg(\dfrac{7}{-\sqrt{15}}\bigg)\rightarrow \quad \theta = \large\boxed{119^o}[/tex]

23) x = -13,   y = 6,   r = [tex]\sqrt{205}[/tex]

     [tex]\tan \theta=\dfrac{y}{x} \rightarrow \quad \tan \theta =\dfrac{6}{-13} \rightarrow \quad \theta = tan^{-1}\bigg(\dfrac{6}{-13}\bigg)\rightarrow \quad \theta = \large\boxed{155^o}[/tex]

24) x = 4,    y = -3,   r = 5

     [tex]\sin \theta=\dfrac{y}{r} \rightarrow \quad \sin \theta =\dfrac{-3}{5} \rightarrow \quad \theta = sin^{-1}\bigg(\dfrac{-3}{5}\bigg)\rightarrow \quad \theta = \large\boxed{323^o}[/tex]

For the point [tex](-\sqrt{17},8)[/tex], [tex]cos\theta=0.4581[/tex]

For the point [tex](3,4)[/tex], [tex]cos\theta=0.6[/tex]

For the point [tex](-\sqrt7,-3)[/tex], [tex]sin\theta=-0.75[/tex]

For the point [tex](-\sqrt{15},7)[/tex], [tex]tan\theta=-1.807[/tex]

For the point [tex](-13,6)[/tex], [tex]tan\theta=-0.4615[/tex]

For the point [tex](4,-3)[/tex], [tex]sin\theta=-0.6[/tex]

For ratios [tex]sin\theta[/tex] and [tex]cos\theta[/tex], we need to calculate the hypotenuse of the right-angled triangle. For the ratio [tex]tan\theta[/tex], we can directly make use of the coordinate points.

For the point [tex](-\sqrt{17},8)[/tex]

[tex]r=\sqrt{17+8^2}=9[/tex]

[tex]cos\theta=\dfrac{x}{r}\\\\=-\dfrac{\sqrt{17}}{9}\approx0.4581[/tex]

For the point [tex](3,4)[/tex]

[tex]r=\sqrt{3^2+4^2}=5[/tex]

[tex]cos\theta=\dfrac{x}{r}\\\\=\dfrac{3}{5}=0.6[/tex]

For the point [tex](-\sqrt7,-3)[/tex]

[tex]r=\sqrt{7+(-3)^2}=4[/tex]

[tex]sin\theta=\dfrac{y}{r}\\=-\dfrac{3}{4}=-0.75[/tex]

For the point [tex](-\sqrt{15},7)[/tex]

[tex]tan\theta=\dfrac{y}{x}\\=-\dfrac{7}{\sqrt{15}}=-1.807[/tex]

For the point [tex](-13,6)[/tex]

[tex]tan\theta=\dfrac{y}{x}\\=-\dfrac{6}{13}=-0.4615[/tex]

For the point [tex](4,-3)[/tex]

[tex]r=\sqrt{4^2+(-3)^2}=5[/tex]

[tex]sin\theta=\dfrac{y}{r}\\=-\dfrac{3}{5}=-0.6[/tex]

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Answer:

  f(x) = x^3 -5x^2 +25x -125

Step-by-step explanation:

For zero x=a, one of the factors is (x -a). If the polynomial has integer coefficients, its complex roots come in conjugate pairs. So, the roots are ...

  roots: -5i, 5i, 5

  factors: (x -(-5i))(x -5i)(x -5)

Multiplying these out gives your polynomial as ...

  f(x) = (x^2 +25)(x -5)

  f(x) = x^3 -5x^2 +25x -125

Answer: 2.2532

Step-by-step explanation:

From the table attached :

Expected probability = sum of p(x) * x ; wher P-X) is the probability of x

E(p(x), x) = (0*0) + (1 * 0.06) *(2*0.1) + (3 * 0.16) * (4 *0.16)+ (5*0.26) * (6 *0.08) + (7 * 0.13) + (8 * 0.05)

Pp(x) * x) = 2.2532

Therefore, the expected value of the distribution is 2.2532

Answer:

2m  

4

−2m  

3

−26m  

2

−23m+20

Step-by-step explanation:

Answer:

1) A. y= (20 - 2x) /5

2) C. 141.3

3) True ( Your answers are here.)

Answer:

1. is A 2. is C 3. is I believe True

Step-by-step explanation:

1.

2x + 5y = 20

-2x          -2x

5y = 20 - 2x

/5          /5

Answer: y = 20 - 2x /5

2.

V = πr^2h

π=3.14  r=3  h=5

3.14*3^2*5

1.413*10^2 which = 141.3

3.

I am not completely sure but I think it is True

Hope this helps