find the area of quadrilateral​

Answer:

The team won 144 gold medals

Step-by-step explanation:

A fraction tells us how many parts of a whole we have

144 / 360 translated into words is 144 out of 360

144 is the part and the 360 is the whole (total)

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x = 90°

2x = 180°

Step-by-step explanation:

angle VTS= angle TSR (alternate angle)

now in ∆TRS,

2x + x + x = 360° (angle sum property of ∆)

4x = 360°

x = 90°

Answer:

D. 41

Step-by-step explanation:

To solve, you have to clear "x" from the equation by dividing the other side of the equation by 22:

The only solution for 22x=901 is 41

Answer: x=41

Step-by-step explanation:

Hii!

Do you need to know the solution set of 22x=902? No problem! (:

We just need to divide both sides by 22 to solve for "x".

x=41; this equation has one solution only

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Hope that this helped! Best wishes.

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The average rate of change of f(x) = -3x² + 1 over each of the given intervals are; -18, 6 nd 38

We are given the function;

f(x) = -3x² + 1

(a) From 2 to 4;

f(2) = -3(2)² + 1

f(2) = -12 + 1

f(2) = -11  (2, -11)

f(4) = -3(4)² + 1

f(4) = -47  (4, -47)

Slope = (-47 - (-11))/(4 - 2)

Slope = -36/2

Slope = -18

(B) From -2 to 0;

f(-2) = -3(-2)² + 1

f(2) = -12 + 1

f(2) = -11  (-2, -11)

f(4) = -3(0)² + 1

f(4) = 1  (0, 1)

Slope = (1 - (-11))/(0 - (-2))

Slope = 12/2

Slope = 6

(C) From 2 to 5;

f(2) = -3(2)² + 1

f(2) = -12 + 1

f(2) = -11  (2, -11)

f(5) = -3(5)² + 1

f(5) = -74  (0, -74)

Slope = ((-74) - 2)/(0 - 2)

Slope = -76/-2

Slope = 38

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Using it's concept, it is found that there is a 0.1541 = 15.41% probability that the first three balls are drawn out of the box alternated in colour.

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

Considering the situation described, the ways that alternate colored balls can be taken with the probabilities given as follows:

Hence the probability that the first three balls are drawn out of the box alternated in colour is given by:

[tex]p = \frac{5}{8} \times \frac{3}{9} \times \frac{5}{11} + \frac{3}{8} \times \frac{5}{10} \times \frac{5}{11} = 0.0689 + 0.0852 = 0.1541[/tex].

0.1541 = 15.41% probability that the first three balls are drawn out of the box alternated in colour.

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See attached images for work.

Answer:

$46,819 is the average unemployed salary

A function assigns the values. The function g(x) can be written as g(x) = -3x + 12.

A function assigns the value of each element of one set to the other specific element of another set.

Given the function f(x)=-x, now since a transformed function g(x) is produced by shifting the function 4 units upwards and vertical stretch by a factor of 3. Therefore, g(x) can be written as,

Vertical Shift by 4 units,

f(x)+4

Vertical stretch by a factor of 3

g(x) = 3(f(x) + 4)

g(x) = -3x + 12

Hence, the function g(x) can be written as g(x) = -3x + 12.

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which of the following sets are discrete?

Answer: C. {2,4,6,8}

Step-by-step explanation:

because constituting a separate entity : individually distinct several discrete sections. 2a : consisting of distinct or unconnected elements : noncontinuous. b : taking on or having a finite or countably infinite number of values discrete probabilities a discrete random variable.

Answer:

[tex](x^{2} +2)-3\\x^{2} +2-3\\x^{2} -1\\(x+1)(x-1)[/tex]

Answer:

x^2+4x+1

Step-by-step explanation:

(x+2)^2-3

(x+2)(x+2)-3

x^2+2x+2x+4-3

x^2+4x+4-3

x^2+4x+1

Answer:

409

Step-by-step explanation:

296 = 200 + 90 + 6
The value of the 9 is 90 in 296.
1/10 of 90 is 9. The only number that has a 9 in the units digit is 409.

Answer: 4 blue chips (brochure), 6 yellow chips (news article), and 10 red chips (computer presentation).

Step-by-step explanation: If you have 20 colored chips, then 20% of the people that chose the brochure will be 20% of 20 of the chips. That is 20 * 0.2 = 4. Now, to find how to model the people who chose the news article, it will be 30% of the 20 chips. That is 20 * 0.3 = 6. Thus, 6 chips can be modeled for the news articles. Lastly, we add 6 + 4 and that is 10. The rest is another ten out of the 20. Thus, we can use 10 red chips to model the computer presentation.

The teacher should use 4 blue chips for the making a brochure option, 6 yellow chips for the writing a news article option, and 10 red chips for the designing a computer presentation option.

A division is a process of splitting a specific amount into equal parts.

To model this situation using colored chips, we can use the following approach:

Divide the total number of chips (20) into five equal parts, each representing 20% of the total number of students.

For the making a brochure option, use four blue chips to represent the 20% of students who choose this option.

For the writing a news article option, use six yellow chips to represent the 30% of students who choose this option.

For the designing a computer presentation option, use ten red chips to represent the remaining 50% of students who choose this option.

So, the teacher should use 4 blue chips for the making a brochure option, 6 yellow chips for the writing a news article option, and 10 red chips for the designing a computer presentation option.

Hence,  the teacher should use 4 blue chips for the making a brochure option, 6 yellow chips for the writing a news article option, and 10 red chips for the designing a computer presentation option.

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Answer:

A=30

B=35

C=44

Step-by-step explanation:

The option second "No, they are not independent because P(student)≈ 0.82 and P(student pirate) ≈ 0.94" is the correct option (B) is correct.

It is defined as the ratio of the number of favorable outcomes to the total number of outcomes, in other words, the probability is the number that shows the happening of the event.

We have a table given that shows the survey asks teachers and students whether they would like the new school mascot to be a pirate or a moose.

The probability of a person that is a student:

P(student) = (75+15)/110 = 0.83

The probability:

P(student|pirate) = 75/80 = 0.93

The probability of both events is different.

Thus, the option second "No, they are not independent because P(student)≈ 0.82 and P(student pirate) ≈ 0.94" is the correct option (B) is correct.

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Answer: [tex]\sqrt[4]{64}[/tex]

Step-by-step explanation:

[tex]64^{\frac{1}{4} }= \sqrt[4]{64}[/tex]

Answer:

y=160

Step-by-step explanation:

y=90+14(x)

x=5

y=90+14(5)

y=90+70

y=160

Hope this helps!

If not, I am sorry.

The denominator of the simplified expression will be (9n² + 4).

A fraction number is a number that represents the part of the whole, where the whole can be any number. It is in the form of numerator and denominator.

The expression is given below.

[(2 / 6n + 4)] [(3n + 2) / (3n – 2)]

On multiplication, we have

(6n + 4) / (18n² + 8)

(3n + 2) / (9n² + 4)

The denominator of the simplified expression will be (9n² + 4).

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It has been proved that the 5 star vertices have their sum of angles as A + B + C + D + E = 180°

The adjoining star contains a regular pentagon. Thus;

Sum of interior angles of the pentagon = (5 - 2) * 180 = 540°

Thus;

Each interior angle of the pentagon = 540/5 = 108°

Thus, each exterior angle = 180 - 108 = 72°

Then measure of the angle at the vertex = 180 - 72 - 72 = 36°

Thus, each angle at the vertices of the star have an angle of 36°.

There are 5 star vertices and so;

Sum of angles of 5 star vertices = 5 * 36 = 180°

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Answer:

b

Step-by-step explanation:

eq y=x+4 is for x>=2 inclusive

Answer:

f(1) = 2

f(n) = 2 × f(n - 1) , n ≥ 2

Step-by-step explanation:

the point of coordinates (1 , 2) is on the graph

Then

f(1) = 2

…………………………

We notice that :

f(2) = 4

f(3) = 8

f(4) = 16

16/8 = 8/4 = 4/2 = 2/1 = 2

________________________

This means the common ratio

of the geo sequence = 2

Hence ,

f(n) = 2 × f(n - 1)

Answer: f(n) = 2 × f(n - 1) , n ≥ 2

Step-by-step explanation:

Answer:

14.3 km  (1 d.p.)

Step-by-step explanation:

To find the mean, divide the sum of all data values by the total number of data values.

If Mark ran a mean distance of 13.2 km in five days, we can use the mean distance for each of the 5 days in our calculation.

[tex]\begin{aligned}\implies \sf mean\:distance & = \sf \dfrac{13.2+13.2+13.2+13.2+13.2+20}{6}\\ & \sf =\dfrac{86}{6}\\\\ & = \sf 14.3\:km\:\:(1\:d.p.)\end{aligned}[/tex]

The numbers should be 2, 2, 5, 9 and 12.

The arithmetic mean is found by adding the numbers and dividing the sum by the number of numbers in the list.

The median is the middle value in a list ordered from smallest to largest. The mode is the most frequently occurring value on the list.

Let us take numbers 2, 2, 5, 9 and 12.

mean = 30/5

mean= 6

range = 10.

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Answer:

I'm not sure what the question is.    I'll offer one simplification that might help.

Step-by-step explanation:

[tex]\sqrt{3} - 3(4*\sqrt{8})[/tex]

One can convert the [tex]\sqrt{8}[/tex] to [tex]\sqrt{2} *\sqrt{4}[/tex] and then that becomes [tex]\sqrt{2} *\2}[/tex]2 or 2[tex]\sqrt{2}[/tex]

[tex]\sqrt{3} - 3(4*\sqrt{2}\sqrt{4})\\[/tex]

[tex]\sqrt{3} - 3(4*2*\sqrt{2})\\[/tex]  See above explanation.

[tex]\sqrt{3} - 24*\sqrt{2})\\[/tex]

Answer:

y = 4x - 17

Step-by-step explanation:

y - 3 = 4(x - 5) ← distribute parenthesis by 4

y - 3 = 4x - 20 ( add 3 to both sides )

y = 4x - 17

Step-by-step explanation:

As far as I understand, they can use all 26 letters (alphabet) and all 10 digits (0, 1, ..., 9), and the password looks like this:

letter-letter-letter-letter-letter-letter-number-number (6 letters, 2 numbers).

▪︎ They can reuse the letters, so they can choose the 1st letter out of 26 possible letters, then they still can choose the 2nd letter out of 26 (it's ok if they have both A's for example, they can reuse them) and so on. So each time they can choose one letter out of 26. Thus, it's 26*26*26*26*26*26.

▪︎ The same thing with numbers. Each time they can choose one number out of 10, so it's 10*10.

▪︎ Therefore, the answer is 26*26*26*26*26*26*10*10 = 30,891,577,600. That's almost 31 billion passwords.

Answer:

y = (- 2/3)x - 3

Step-by-step explanation:

y = mx + c

y = (- 2/3)x + c

- 1 = (- 2/3)(-3) + c

-1 = 2 + c

c = - 3

Therefore,

y = (-2/3)x - 3

Answer:

y = -2/3x - 3

Step-by-step explanation:

y = mx + b

y = y coordinate              → given: - 1

m = slope                        → given: - 2/3

x = x coordinate              → given: - 3

b = y intercept                 → need to find

y = -2/3x + b → -1 = -2/3(-3) + b

-1 = 2 + b

subtract 2 from both sides

-1 - 2 = 2 - 2 + b

-3 = b

y = -2/3x - 3

The choice trigonometric ratio is tangent and the distance is 3. 98 meters.

The given angle is 86

The opposite side is given as 57 meters

The distance is in the adjacent

Thus, trigonometric ratio to use is the tangent

Tangent = opposite/ adjacent

We have,

tan 86 = 57/x

14. 300 = 57/x

x = 57/ 14. 300

x = 3.i 98 meters

Thus, the choice trigonometric ratio is tangent and the distance is 3. 98 meters.

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