Henry constructed circle A with a radius of 4 units. He then created a sector
as shown in the figure below. Which of the following expressions would help
him find the area of the shaded sector?

Answer:[tex]a^2-b^2=3[/tex]

Step-by-step explanation:

We need to find the value of the below expression i.e.

[tex]a^2-b^2[/tex] when a = 2 and b = 1.

So,

Put a = 2 and b = 1 in the above expression. So,

[tex]a^2-b^2=(2)^2-1^2\\\\=4-1\\\\=3[/tex]

Hence, the value of the expression is equal to 3.

Answer:

z=9

Step-by-step explanation:

we are given: 2/3z=6

we need to find what z is by itself

6 is 2/3rds of what the value of z is.

to find z, we need to multiply both sides by 3/2 (the reciprocal of 2/3z, to make the coefficient of 1)

3/2*2/3z=6*3/2

z=9

hope this helps :)

z = 9

Step-by-step explanation:

2/3 . z = 6

2z/3 = 6

Multiple all terms by the same value to eliminate fraction denominator,

3 x 2z/3 = 3 x 6

2z = 18 ( 3,3 got cancelled)

Divide both sides of the equation by the same term,

2z/2 = 18/2

On Simplify,

z = 9.

*(2,2 gets cancelled and 18/2 = 9)

Answer:

a. Outcomes of A = { (C,C,C) , (D,D,D), (S,S,S) }

b. Outcomes of B = { (C,D,S),(C,S,D),(D,C,S),(D,S,C),(S,C,D),(S,D,C) }

c. Outcomes of C = { (C,C,C),(C,C,D),(C,C,S),(C,D,C),(C,S,C),(D,C,C),(S,C,C) }

d. Outcomes of A⋂C = { (C,C,C) }

e. Outcomes of Sample space = { (C,C,C), (C,C,D), (C,C,S), (C,D,C), (C,D,D), (C,D,S), (C,S,C), (C,S,D), (C,S,S), (D,C,C), (D,C,D),(D,C,S), (D,D,C), (D,D,D), (D,D,S), (D,S,C), (D,S,D), (D,S,S),   (S,C,C), (S,C,D), (S,C,S), (S,D,C), (S,D,D), (S,D,S), (S,S,C), (S,S,D), (S,S,S) }

f. Outcomes of A U B = { (C,C,C) , (D,D,D), (S,S,S), (C,D,S),(C,S,D),(D,C,S),(D,S,C),(S,C,D),(S,D,C) }

g. Outcomes of A⋂[tex]C^{c}[/tex] = { (D,D,D), (S,S,S) }

h. Outcomes of [tex]A^{c}[/tex]⋂C = {(C,C,D),(C,C,S),(C,D,C),(C,S,C),(D,C,C),(S,C,C)}

i. Events A and C are not mutually exclusive

j. Events B and C are mutually exclusive

Step-by-step explanation:

Given - Three times each day, a quality engineer samples a component

             from a recently manufactured batch and tests it. Each part is

             classified as conforming (suitable for its intended use),  

             downgraded (unsuitable for the intended purpose but usable for  

             another purpose), or scrap (not usable). An experiment consists

             of recording the categories of the three parts tested in a particular

              day.

To find - a. Let A be the event that all the parts fall into the same

                  category. List the outcomes in A.

              b. Let B be the event that there is one part in each category.

                  List the outcomes in B.

              c. Let C be the event that at least two parts are conforming.

                  List the outcomes in C.

              d. List the outcomes in A⋂C

              e. List the 27 outcomes in the sample space.

               f. List the outcomes in A U B.

              g. List the outcomes in A⋂[tex]C^{c}[/tex]

              h. List the outcomes in ⋂C.

              i. Are events A and C mutually exclusive? Explain.

              j. Are events B and C mutually exclusive? Explain.

Proof -

Let

Conforming part = C

Downgraded part = D

Scrap part = S

a.)

Given , Let A be the event that all the parts fall into the same category.

Outcomes of A = { (C,C,C) , (D,D,D), (S,S,S) }

b.)

Given, Let B be the event that there is one part in each category.

Outcomes of B = { (C,D,S),(C,S,D),(D,C,S),(D,S,C),(S,C,D),(S,D,C) }

c.)

Given,  Let C be the event that at least two parts are conforming.

Outcomes of C = { (C,C,C),(C,C,D),(C,C,S),(C,D,C),(C,S,C),(D,C,C),(S,C,C) }

d.)

Outcomes of A⋂C = { (C,C,C) }

e.)

Outcomes of Sample space = { (C,C,C), (C,C,D), (C,C,S), (C,D,C), (C,D,D), (C,D,S), (C,S,C), (C,S,D), (C,S,S), (D,C,C), (D,C,D),(D,C,S), (D,D,C), (D,D,D), (D,D,S), (D,S,C), (D,S,D), (D,S,S),   (S,C,C), (S,C,D), (S,C,S), (S,D,C), (S,D,D), (S,D,S), (S,S,C), (S,S,D), (S,S,S) }

f.)

Outcomes of A U B = { (C,C,C) , (D,D,D), (S,S,S), (C,D,S),(C,S,D),(D,C,S),(D,S,C),(S,C,D),(S,D,C) }

g.)

Outcomes of [tex]C^{c}[/tex]  =  {  (C,D,D), (C,D,S), (C,S,D), (C,S,S), (D,C,D),(D,C,S), (D,D,C), (D,D,D), (D,D,S), (D,S,C), (D,S,D), (D,S,S), (S,C,D), (S,C,S), (S,D,C), (S,D,D), (S,D,S), (S,S,C), (S,S,D), (S,S,S) }

Outcomes of A⋂[tex]C^{c}[/tex] = { (D,D,D), (S,S,S) }

h.)

Outcomes of [tex]A^{c}[/tex] = {(C,C,D), (C,C,S), (C,D,C), (C,D,D), (C,D,S), (C,S,C), (C,S,D), (C,S,S), (D,C,C), (D,C,D),(D,C,S), (D,D,C),  (D,D,S), (D,S,C), (D,S,D), (D,S,S),   (S,C,C), (S,C,D), (S,C,S), (S,D,C), (S,D,D), (S,D,S), (S,S,C), (S,S,D), }

Outcomes of [tex]A^{c}[/tex]⋂C = {(C,C,D),(C,C,S),(C,D,C),(C,S,C),(D,C,C),(S,C,C) }

i.)

As we two that Two events A and C are mutually exclusive iff A ∩ C = ∅

Now,

A ∩ C = { (C,C,C) }

⇒Events A and C are not mutually exclusive.

j.)

As we two that Two events B and C are mutually exclusive iff B ∩ C = ∅

Now,

B ∩ C = ∅

⇒Events B and C are mutually exclusive.

Answer:

Check pdf

Step-by-step explanation:

Answer:

X= 6.2 + 68 ???

Step-by-step explanation:

I'm not sure that's what I would write in an exam

Answer:

4000

Step-by-step explanation:

36kg = 36000g

36000g/9 bags = 4000g

The weight of one bag of potatoes is 4 Kg,

The unitary technique involves first determining the value of a single unit, followed by the value of the necessary number of units.

For example, Let's say Ram spends 36 Rs. for a dozen (12) bananas.

12 bananas will set you back 36 Rs. 1 banana costs 36 x 12 = 3 Rupees.

As a result, one banana costs three rupees. Let's say we need to calculate the price of 15 bananas.

This may be done as follows: 15 bananas cost 3 rupees each; 15 units cost 45 rupees.

Given:

The total weight of 9 bags of potatoes is 36 kilograms.

Then, weight of one bag of Potato is

= 36/9

= 4 Kg

Thus, One bag weigh 4 Kg.

Learn more about Unitary Method here:

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Answer:

The second one

Step-by-step explanation:

Answer:

Is the third one,as you can see it goes thru the point (2,5)

Step-by-step explanation:

to find the area of the rectangle it is is length x width  so we do 3x4=12. then area of triangle is base x height divide by 2, so 2x4=8. 8 divide by 2 is 4, then we need to add them all up, so 12 + 4 + 4 is 20. Your answer is 20 cm2.

(Ps please mark brainliest i need for next rank)

The measure of <1 and <2 are  alternate exterior angles

From the given diagram, the horizontal lines are parallel to each other with a transversal.

The alternate angles are formed from the shape formed by a letter Z. From the given diagram, the measure of <1 and <2 are  alternate exterior angles

Learn more on exterior angles here: https://brainly.com/question/17972372

Answer:

what is the question....?

Answer:

Answer:We need to know the question!!

Answer:

7 or -7

Step-by-step explain

This depends on how it works. if we are including negative numbers then an option is -7. If we are going backwards and not including negatives then it would be 7

Answer:

6) K is less than negative seven.

7) m is less than or equal to two and three fifths.

Step-by-step explanation:

Answer:

I THINK the first and second choice, because it said the last two digits are between the numbers 0-9, them two are the only ones that end with them.

Step-by-step explanation:

You have a nice day to!!

Answer:

0.35 or 35%

Step-by-step explanation:

The probability that any seed will germinate is said to be 0.65 (or 65%) in the question. This means that the remaining percentage is the probability that the randomly selected seed will not germinate. This is because there is only two possible outcomes to that given scenario, which is it will germinate or not. Meaning that the remaining percentage/probability is that it will not germinate

1 - 0.65 = 0.35 or 35%

Answer:

139

Step-by-step explanation:

x^2 + y^3 2+x = 3^2 + 5^3 + 2 + 3

= 9 + 125 + 5

= 139!

Answer:

x-6=6

Step-by-step explanation:

6+6=12

Answer:

c

Step-by-step explanation:

because 6+6=12 and the missing number would be 12 because 12-6=6

Answer:

133

Step-by-step explanation:

180 - 47 = 133

Answer:

133°

Step-by-step explanation:

If we assume the the given to adjacent lines to be parallel then ,

Therefore :-

=> x = 180° - 47°

=> x = 133° .

Explanation:

You can verify this by plugging each root into the equation.

So for instance, plug in x = -2 and we get

f(x) = -3*(x+2)*(x-sqrt(3))*(x-4)

f(-2) = -3*(-2+2)*(-2-sqrt(3))*(-2-4)

f(-2) = -3*(0)*(-2-sqrt(3))*(-2-4)

f(-2) = 0

This verifies x = -2 is a root.

All that matters is that zero buried in there in the second to last step. Multiplying 0 by anything leads to 0. The other roots are verified in the same manner. The -3 out front is the leading coefficient.

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

Extra info:

Answer:

1. Trapezoid.

2. Rectangle, Parallelogram

3. Rhombus, Parallelogram

4. Rectangle, Parallelogram, Square

5. No, a figure cannot have more than one parallel side and exactly one parallel side at once.

Step-by-step explanation:

Hope ths helped.

Answer:

19.1

Step-by-step explanation:

i took the testttttt

Perimeter is the sum of the length of the sides used to make the given figure. The perimeter of the given shape is 19.1 units.

The distance or length of any line on the graph,

[tex]{\rm Distance} = \sqrt{(x_2-x_1)^2 + (y_2-y_1)^2}[/tex]

where,

d = distance or length of the line between points 1 and 2,

(x₁ , y₁) = coordinate of point 1,

(x₂ , y₂) = coordinate of point 2,

To find the perimeter of the given figure we need to calculate the length of each line segment on the given graph. Therefore, the length of the different sides of the given quadrilateral can be written as,

AB = √[(5-0)²+(-1-0)²] = √26 units

BC = √[(5-3)²+(-1+5)²] = √20 units

CD = √[(3+2)²+(-5+4)²] = √26 units

AD = √[(-4 - 0)²+(- 2 - 0)²] = √20 units

Perimeter = AB + BC + CD + AD

                 = √26 units + √20 units + √26 units + √20 units

                 = 19.1423 units ≈ 19.1 units

Hence, the perimeter of the given shape is 19.1 units.

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Answer:

24+12=36you find the total length

Answer:

3 feet

Step-by-step explanation:

Answer:

x=-3

Step-by-step explanation:

How?

so the easiest and quickest way to answer these type of questions are to do the opposite.

so -11+8=-3

if you get a question like

3x+2=17

17-2=15

15 divided by 3=5

so x=5

hope that helps

thank you

Answer:

The Pythagorean theorem only works for right triangles. This is not a right triangle.

x = 23

All interior angles of a triangle = 180 degrees.

 A  +      B      +     C    + 180

(3x) + (2x+12) + (2x+7) = 180

7x + 19 = 180

7x = 161

x = 23

A = 3(23) = 69 degrees

B = 2(23) + 12 =58 degrees

C = 2(23) + 7 = 53 degrees

Answer:

x=23

Step-by-step explanation:

u see this is how the Pythagorean theorem works a^2 + b^2 = c^ i hope this helps have a great day bye please mark as brainliest :D

Answer:

32 cats in total

Step-by-step explanation:

so 18 siamese

the ratio was9:7=siameese:house

18=9 units

divide 9

2=1 unit

house=7 units

7 times 2=14

14 house cats

combined=siameese+house=18+14=32