acyclics

Part A. 33

Part B. 8

Part C. 145

Step-by-step explantion:

Part A:

If there were 29 students in band.  This includes the 9 in both band and drama; this leaves 20 in only band.  

There were 17 students in drama.  This includes the 9 in both band and drama; this leaves 8 in only drama.

There were 70 students sampled; this means that

70-(20+8+9) = 70-37 = 33 students in neither band nor drama.

Part B:

There were 8 in only drama.

Part C:

Since there were 29/70 in band, this means the director can assume he will have

29/70(350) = 29/70(350/1) = 10150/350 = 145 to show up the first day.

Median = 6

Lower quartile =  4

Upper quartile = 7.5

Interquartile range = 3.5 

Step-by-step explanation:

Well you can refer to my attached photo ( cannot believe I am answering my own question )

arrange the data from least to greatest: 

Mar Feb May Jan Apr

3       5      6     7     8

( 6 is the median v/ )

Lower quartile: 5 if you split it you can see how it is made. ( Like in picture )

( 4 is the LQ v/ )

Upper quartile: 5 if you split it you can see how it is made. ( Like in picture [ like above ] )

( 7.5 is the UQ v/ )

Interquartile range:

= UQ - LQ = 7.5 - 4 = 3.5

( 3.5 is the IQ Range v/ )

Thus the answers to MY problem is:

Median = 6

Lower quartile =  4

Upper quartile = 7.5

Interquartile range = 3.5 

URL for picture ( if it doesnt load ):

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The probability that the distance between two points on a circle of radius 1 is at most 1.5 is approximately 0.477 or 47.7%, which corresponds to the range of central angles less than or equal to 3 radians out of the total central angle of 2π radians.

Step-by-step explanation:

Let's consider two points on a circle of radius 1, labeled A and B. The distance between A and B is given by the length of the arc AB on the circle, which is a fraction of the circumference of the circle. The circumference of a circle of radius 1 is 2π, so the length of the arc AB is given by

d = θ/2π * 2πr = θ

where d is the distance between A and B, θ is the central angle between A and B (in radians), and r is the radius of the circle (which is 1 in this case).

To find the probability that the distance between A and B is at most 1.5, we need to find the range of central angles that correspond to arc lengths less than or equal to 1.5. Let's call this range of angles θ₁. We have

θ₁ = 2d/r = 2(1.5)/1 = 3

This means that the central angle between A and B must be less than or equal to 3 radians for the distance between A and B to be at most 1.5. Since the total central angle of the circle is 2π radians, the probability of selecting two points with a central angle less than or equal to 3 radians is

P(θ ≤ 3) = θ/2π = 3/2π ≈ 0.477

Therefore, the probability that the distance between two points on a circle of radius 1 is at most 1.5 is approximately 0.477 or 47.7%.

We know that the angle bisector theorem and the specified requirements are satisfied if BC = 16, CZ = 8, and BZ = 24. The angle bisector theorem is also satisfied if BC = 8, which also makes CZ = 16/3 and BZ = 112/9.

Step-by-step explanation:

What is angle bisector theorem?

The opposite side of a triangle is divided into two portions that are proportional to the sides they are on if the angle is bisected by a line, according to the angle bisector theorem.

The angle bisector theorem, which asserts that if a line bisects a triangle's angle, it divides the opposite side into two segments that are next sides to each other, can be used to solve this problem.

Let BC and BZ both equal x. The angle bisector theorem provides us with:

AC/AB = CZ/BZ

16/(16+x) = 16/y

We solve y in terms of x, and as a result,

y = 16(16+x)/16 = x+16

Upon substitution, we discover—

16/(16+x) = 16/(x+16)

If we cross-multiply, we obtain:

16(x+16) = 16(16+x)

Simplifying, we get:

16x + 256 = 256 + 16x

In light of the fact that 16x cancels on both sides, we are left with:

256 = 256

As a result, there exist an endless number of BC and BZ values that could satisfy the requirements.

The answer to your problem is, 0.01

Step-by-step explanation:

Least count of a s***w gauge is given as,

LC = \({Pitch \over Number..Of..Divisions..On..Circular..Scale}\)

= \( {0.5\over 50}\)

= 0.01

Thus the answer to your problem is, 0.01

The answer to your problem is, 480

Step-by-step explanation:

Multiply:

\(^3\sqrt{576000*4*48}\)

\(^3\sqrt{110592000}\)

Evaluate:

\(^3\sqrt{110592000}\)

= 480

480 being the answer

Thus the answer to your problem is, 480

The candy bar cost, in dollars, is $1.05

Step-by-step explanation:

Say the price of a piece of bubble gum is x.

This means that we can represent our scenario with the equation (x+1)+x=1.10, with (x+1) representing the price of a candy bar. 

We can then solve from there.

We have given that,

(x+1)+x=1.10

Simplify above expression

2x+1=1.10 

2x=0.10 - Subtract From Both Sides

x=0.05 - Divide From Both Sides

So now we have the price of the piece of bubble gum, but we want the cost of the candy bar.

What is the cost?

Cost is the value of money that a company had to spend to produce its goods or services.

Fortunately, we know it costs one dollar more than the piece of bubble gum,so just do 0.05 + 1. This means our candy bar costs $1.05.

The answer to your problem is, 8

Step-by-step explantion:

1/2 can be represented as 0.5 so here is the new equation:

0.5 x ? = 4

well:

4 / 0.5 = 8

8 being the answer

Thus the answer to your problem is, 8

From the first piece of information, we can set up an equation:

D - 7 = 9(G - 7)

Simplifying this equation, we get:

D - 7 = 9G - 63

D = 9G - 56

From the second piece of information, we can also set up an equation:

D - 6 = 7(G - 6)

Simplifying this equation, we get:

D - 6 = 7G - 42

D = 7G - 36

Now we can combine the two equations:

9G - 56 = 7G - 36

Solving for G, we get:

2G = 20

G = 10

So currently, Grogg is 10 years old. We can substitute this value back into either equation to find his dad's age:

D = 9G - 56

D = 9(10) - 56

D = 34

Therefore, Grogg's dad is currently 34 years old.

The side length of the square PZXY is sqrt(2).

Step-by-step explanation:

What is a square?

A square is a two-dimensional figure that has four sides and all four sides are equal.

The area of a square is given as side².

We have,

Since triangle PQR is a right triangle, we can use the Pythagorean theoremto find the length of QR:

QR² = PQ² + PR²

QR² = 1² + 1²

QR² = 2

QR = √2

Since PZXY is a square, its sides are equal in length. 

Let's denote the length of one side of the square as s. 

Then, we can write:

PR = PX + RX

1 = s + QY

Since QY = PZ = s and PX = QX = QR - QY = sqrt(2) - s, 

we can substitute these values into the equation for PR to get:

1 = s + (√2 - s)

1 = √2

Therefore, 

The side length of the square PZXY is √2.