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Answer:

a) 52.0 cm

b) 62.8 cm

c) 114.8 cm

Conversion:

120° = 2π/3 radians

(a) Find Length of chord PR;

⇒ 2(radius)sin(θ/2)

⇒ 2(30)sin((2π/3)/2)

⇒ 2(30)sin((2(3.142)/3)/2)

⇒ 30√3

⇒ 52.0 cm

(b) Find Length of arc PQR;

⇒ radius(θ)

⇒ 30(2π/3)

⇒ 30(2(3.142)/3)

⇒ 62.8 cm

(c) The perimeter of shaded region;

⇒ Length of chord + Length of arc

⇒ 62.84 + 51.965

⇒ 114.8 cm

Answer:

(a)  52.0 cm

(b)  62.8 cm

(c)  115 cm

Step-by-step explanation:

Part (a)

[tex]\textsf{Chord length}=2r \sin \left(\dfrac{\theta}{2}\right)[/tex]

where:

Given:

Substitute the given values into the formula:

[tex]\begin{aligned}\implies PR & =2(30)\sin \left(\dfrac{120^{\circ}}{2}\right)\\\\& = 30\sqrt{3}\\\\ & = 52.0\:\sf cm\:(3\:sf)\end{aligned}[/tex]

Part (b)

[tex]\textsf{Arc length}=2 \pi r\left(\dfrac{\theta}{360^{\circ}}\right) \quad[/tex]

where:

Given:

Substitute the given values into the formula:

[tex]\begin{aligned}\implies PQR & =2 (3.142)(30)\left(\dfrac{120^{\circ}}{360^{\circ}}\right) \quad\\\\ & = \dfrac{1571}{25}\\\\ & = 62.8 \sf \:\:cm \:(3 \:sf)\end{aligned}[/tex]

Part (c)

[tex]\begin{aligned}\textsf{Perimeter of shaded portion} & = \textsf{chord length} + \textsf{arc length}\\\\ & = 30\sqrt{3}+\dfrac{1571}{25}\\\\ & = 114.80152...\\\\ & = 115\:\: \sf cm\:(3\:sf)\end{aligned}[/tex]

The value of x is 6 and the value of k is 2.5. The correct option is the last option - 2.5

From the question, we are to determine the value of k, that is, the constant of proportionality

From the given information,

y varies jointly with x and z

Mathematically, this can be written as

y ∝ xz

Then, introducing the constant of proportionality, k, we get

y = kxz

Also, from the given information

y = 200 when x = 8 and z = 10

Putting these values into the equation, we get

200 = k × 8 × 10

200 = 80k

∴ k = 200/80

k = 2.5

Now, for the value of x when y = 165 and z = 11

Using the equation

y = kxz

Then, put the parameters into the equation

165 = 2.5 × x × 11

165 = 27.5x

∴ x = 165 / 27.5

x = 6

Hence, the value of x is 6 and the value of k is 2.5. The correct option is the last option - 2.5

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Answer: 2.5

Step-by-step explanation: I did the quiz

Answer:

iii) R2

Step-by-step explanation:

The probability of the spinner landing on whistle during Edgar's turn is 4/9

The experimental results are given as:

3 glow sticks, 5 bouncy balls, 8 whistles, and 2 foam gliders

The total number of sample is:

Sample = 3 + 5 + 8 + 2

Sample = 18

The probability that Edgar's spin land on whistle is:

P(Whistle) = Whistle/Sample

This gives

P(Whistle) = 8/18

Evaluate

P(Whistle) = 4/9

Hence, the probability of the spinner landing on whistle during Edgar's turn is 4/9

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Answer:

B) 24 feet

General Formulas and Concepts:
Pre-Algebra

Order of Operations: BPEMDAS

Algebra I

Functions

Step-by-step explanation:

Step 1: Define

Identify given.

[tex]\displaystyle h(t) = -16t^2 + 35t + 5[/tex]

Step 2: Find Height

Since we are trying to find the height of the basketball at 1 second, it implies that t = 1. Therefore, we can simply substitute t = 1 into our function:

[tex]\displaystyle\begin{aligned}h(1) & = -16(1)^2 + 35(1) + 5 \\& = -16(1) + 35(1) + 5 \\& = -16 + 35 + 5 \\& = \boxed{24} \\\end{aligned}[/tex]

∴ the height of the basketball at 1 second is equal to 24 feet.

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Topic: Algebra I

2 2/3 of a fraction

________________

2 full and 2/3

- Jackson

Answer:

x = -5

Step-by-step explanation:

-3+x = -8

Add 3 to each side to isolate x

-3+x+3 = -8+3

x = -5

Answer:

72.828

Step-by-step explanation:

h=V

π(d

2)2=11211

π·(14

2)2≈72.828

Answer:

I think the volume is 538.51 in^3.

Step-by-step explanation:

I have tried my hardest sorry if i am wrong

Your question is Incomplete. Please read below for the missing content.

Total cards = 8 + 5 = 13

The selections are being made with replacement. Hence,

a) P(G1 and G2) = P(G1)*P(G2) = (8/13)*(8/13) = 0.3787

b) P(Atleast 1 green) = 1 - P(No green) = 1 - (5/13)*(5/13) = 0.8521

c) P(G2 | G1) = P(G2) = 8/13 = 0.6154

Probability with replacement is used for questions where the outcomes are back again to the sample space again. which means that when the object is selected, then its miles changed and returned to the sample space, so the range of elements of the sample space remains unchanged.

Conclusion: The chance of two consecutive attracts without a replacement from a deck of playing cards is calculated because the range of viable successes over the variety of viable results, is expanded together for each case. accordingly, for the primary ace, there may be a 4/52 possibility and for the second there is a 3/51 probability.

Suppose that you have 8 green cards and 5 yellow cards. The cards are well shuffled. You randomly draw two cards with replacements. Round your answers to four decimal places.

G1 = the first card drawn is green

G2 = the second card drawn is green

a. P(G1 and G2) =

b. P(At least 1 green) =

c. P(G2|G1) =

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Answer:

20 feet

Step-by-step explanation:

Perimeter :

Answer: The answer for 16 is -6 and 3

              The answer for 18 is -9 and -4

x^2 + 3x - 18 = 0

(x + 6) (x - 3) = 0

x^2 + 13x + 36

(x + 9) (x + 4) = 0

Answer:

y=[tex]\frac{1}{12} x+\frac{1}{4}[/tex]

Step-by-step explanation:

Answer:

area: 1.9×0.75÷2

0.7125

perimeter: 2+0.75+2.25

5

Answer:

The event space is the number of outcomes in the event you are interested in. The event space for rolling a number less than three is 1 or 2. So the size of the event space is 2. For equally likely outcomes, the probability of an event E can be written P(E).

The number of sample outcomes that are common to the two events would depend on the specific events and the information provided about their sample spaces.

To find the number of sample outcomes that are common to two events, we need to determine the intersection of the two events. The intersection represents the outcomes that satisfy both events simultaneously.

If we know the number of sample outcomes for each individual event, we can find the number of outcomes that are common to both events by finding the smaller of the two numbers.

For example, let's say event A has 50 possible outcomes and event B has 30 possible outcomes. The number of sample outcomes that are common to both events would be the smaller of the two, which is 30 in this case.

Therefore, the number of sample outcomes that are common to the two events would depend on the specific events and the information provided about their sample spaces.

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Answer:

Q = 108°

R = 72°

Step-by-step explanation:

Quadrilateral means this is a four-sided shape. Parallelogram means that both sets of opposite side are parallel, so all the angles are either equal or add up to 180° (supplementary)

The order of the letters matters bc PQRS means that you go along an edge from P to Q, but you have to go thru the middle of the shape to get from P to R. So P and Q add up to 180°.

P + Q = 180°

72° + Q = 180°

Q = 108°

Opposite from each other, across the middle of the shape, P and R are equal.

P = R = 72°

Answer:

Question seven is 14, Question 8 is 16

Step-by-step explanation:

hoped this helped

10 per cent of the animals were snakes in the given question.

The Percentage is defined as representing any number with respect to the 100. It is denoted by the sign %.

Given that:-

The percentage will be calculated as:=

Snake percentage = ( 2 / 20 )  x  100 = 0.1 x 100 = 10 %

Therefore, 10 per cent of the animals were snakes in the given question.

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So it's volume vs water filled graph

For this y should be highest

Observe all 4

In set 1

So set 1 has highest volume

Hence it has greatest radius

Answer:

C

Step-by-step explanation:

because 14 is 7 x 2 the scale factor from the small pyramid to the big pyramid would be 1/2

Answer:

  (b)  1/8

Step-by-step explanation:

You want the ratio of the volume of the small pyramid to that of the larger one, given their base lengths are 7 and 14 units.

The pyramids are presumed to be similar, so the ratio of the sides given is also the ratio of the unmarked sides and the heights. The volume ratio is the cube of this ratio of side lengths:

  smaller/larger sides = 7/14 = 1/2

  smaller/larger volumes = (1/2)³ = 1/8

The ratio of the volume of the small pyramid to the larger is 1/8.

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Answer:

30

Step-by-step explanation:

Answer:

2³ = 8

Step-by-step explanation:

㏒ₐ ᵇ = ⁿ ⇔ aⁿ = b

Answer:

-23x^3+20x^4+25x^2+84x-84

Step-by-step explanation:

1 Expand by distributing sum groups.

4x^2(3x+5x^2-6)-7x(3x+5x^2-6)+14(3x+5x^2-6)

2 Expand by distributing terms.

12x^3+20x^4-24x^2-7x(3x+5x^2-6)+14(3x+5x^2-6)

3 Expand by distributing terms.

12x^3+20x^4-24x^2-(21x^2+35x^3-42x)+14(3x+5x^2-6)

4 Expand by distributing terms.

12x^3+20x^4-24x^2-(21x^2+35x^3-42x)+42x+70x^2-84

5 Remove parentheses.

12x^3+20x^4-24x^2-21x^2-35x^3+42x+42x+70x^2-84

6 Collect like terms.

(12x^3-35x^3)+20x^4+(-24x^2-21x^2+70x^2)+(42x+42x)-84

7 Simplify.

-23x^3+20x^4+25x^2+84x-84

Answer:

1. She should use Length x Width x Height.

2. The unit of the answer is 30.

3. The volume of the box is 30 units.

The change that would increase Susie’s limits is C. increase coverage on bodily injury to $100/300,000 and on property damage to $50,000.

It should be noted that an insurance simply means a form of risk reduction that is taken regarding an asset.

In this case, the change that would increase Susie’s limits is to increase coverage on bodily injury to $100/300,000 and on property damage to $50,000.

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Answer:

-9x² + x - 10

Step-by-step explanation:

To write in a standart form, variables go in an alphabetical order, from highest to lowest exponent. The last thing to write is a number by itself (ex. 10)

Answer: The domain wouldn’t include negative because it’s not possible to backward in time. The studio might limit the domain to numbers less than or equal to 10 because for x > 10 the number of views is unrealistically big. Also, viral marking slow after a while so the functions may not fit the data as well after 10 days.

Answer:

The answer above is the exact same as on edmentum that the teacher put, just so you know.