if 1,000 points are selected randomly inside the square with all points equally likely to be selected, how many of those points are expected to lie inside the circle?

444 students will climb the rock wall.

Given, that A class has 484848 students, one group of 242424 students chooses to play volleyball.

Then the teacher divides the remaining students into as many groups of 555 as possible to shoot baskets.

After that, the remaining students (not on a volleyball or basketball team) climb the rock wall.

Now, we are asked that the students who climb the rock wall

So, from a class of 484848 students if One group of 242424 students is made to play volleyball then there will be 242424 students remaining.

Now, to divide 242424 students into groups of 555 students,

we need to divide 242424 by 555, then we get

242424/555 = 436.8

Now there will be 436 groups of 555 students who will shoot basket and remaining 444 students who will climb the rock wall.

Hence, 444 students will climb the rock wall.

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The rate of interest for Rebekah's account is 5.25%

Given,

The principal amount deposited by Rebekah, P = $1500

The time period of the deposit, T = 21 months = 5/3 years

The simple interest she got after 21 months, SI = $131.25

We have to find the rate of interest, R;

Simple Interest;

Simple interest is a quick and simple formula for figuring out how much interest will be charged on a loan. The daily interest rate, the principle, and the number of days between payments are multiplied to calculate simple interest.

Here,

Simple interest, SI = PRT/100

131.25 = (1500 × R × 5/3) / 100

131.25 = 15R × 5/3

131.25 = 25R

R = 131.25/25

R = 5.25%

That is,

The rate of interest for Rebekah's account is 5.25%

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The value of y is 24 when x is 7.

A ratio is an ordered pair of numbers a and b, written a / b where b does not equal 0.

Given,

There are direct variations

y= 24 when x=2

We need to find value of y when x =7

This can be found by forming an equation.

Let the value of unknown y be a

2/24=7/a

Apply cross multiplication

2a=24(7)

2a=168

We need to divide by 2 on both sides

a=24

Hence the value of y is 24 when x is 7.

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Answer: The answer is 8

Step-by-step explanation: 16 tablespoon is 1 cup now find half of 16. Half of 16 is 8. So 8 tablespoon should be equal 1/2 cup

Answer:

3×10^7

Step-by-step explanation:

Write 30 000 000 in standard form.

=3×10,000,000

=3×10^7

Step-by-step explanation:

this is

3.0 × 10⁷

as 30 000 000 has 7 zeroes (7 sequential and continuously increasing powers of 10 starting with 10¹).

and the first non-zero digit is 3.

Answer:

A. y = -4x

B. y = 20

Step-by-step explanation:

A. y = xk

Where k is constant

Substitute y for -8 and x for 2

-8 = 2k

Divide both sides by 2

-8/2 = 2k/2

-4 = k

k = -4

y = x(-4)

y = -4x

B. y when x = 5

y = 5(-4)

y = 20

Nadia was 1cm off the actual measurement of 5 cm. That is a percent error of 20%.

Sasha was 4 cm off the actual measurement of 100 cm. That’s a percent error of 4%.

From the information, the measurement was 4cm and the actual measurement was 5cm. Therefore, the difference will be:

= 5cm - 1cm

= 4cm

The percentage error will be:

= Difference in measurement / Actual measurement × 100

= 1/5 × 100

= 20%.

The percentage error for Sasha will be:

= 4/100 × 100

= 4%

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The equation of the line that passes through the point (-8,-3) and has a slope of -3/4 is y = -3/4x - 9

From the question, we have the following parameters that can be used in our computation:

Slope, m = -3/4

Points, (x₁, y₁) = (-8, -3)

A linear equation can be represented as

y = slope * x + y-intercept i.e. y = m(x - x₁) + y₁

Substitute the known values in the above equation

So, we have the following equation

y = -3/4(x + 8) - 3

Open the brackets

So, we have the following equation

y = -3/4x - 6 - 3

Evaluate the like terms in the above equation

So, we have the following representation

y = -3/4x - 9

The above equation cannot be further simplified

Hence. the linear equation is y = -3/4x - 9

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For emission of a surface, the average absorptivity of this surface at 1040 K is 0.899705900025.

Knowing that ε1 =0.15 and ε2 = 0.9, we first solve for the average emission, e, as follows:

ε = ε1 [tex]f_λ[/tex] [ λT]  +   ε2 [1- [tex]f_{λ}[/tex](λT)]

is also solved for reference in calculating fλ

(λ*T) = (5 μm)(1040 K)

       = 5200 μm K

[tex]f_{λ}[/tex]= 0.0003921333  when referencing this to a blackbody function.

Moving on, we solve for T1040 using the equation above:

ε = ε1 [tex]f_{λ}[/tex][λT] + ε2[1 -[tex]f_{λ}[/tex]( λT)]

  =0.9 + (0.15-0.9)0.0003921333  

  =0.899705900025

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The rate in mm per hour at which the height of the water is changing when the height of the water is 2mm is 55.2

Given data,

A partially filled inverted cone contains water. The inverted cone has a 16 mm radius. The inverted cone is 18 mm in height. if the water's volume is growing at a pace of 548 cubic millimeters per hour.

The rate in mm per hour at which the height of the water is changing when the height of the water is 2 mm;

r/h = 16/18

    = 8/9

r = 8h/9

The volume of the cone is;

v = [tex]\frac{1}{3}\pi r^2h[/tex]

v = [tex]\frac{1}{3}\pi (8h/9)^2h[/tex]

v =  [tex]\frac{64}{243}\pi h^3[/tex]

Now, differentiating concerning x;

[tex]\frac{dv}{dt}[/tex]= [tex]\frac{d}{dt}[/tex]        [tex]\frac{64}{243}\pi h^3[/tex]

[tex]\frac{dv}{dt}[/tex]=  64π/243*[tex]\frac{d}{dt}[/tex] h³

[tex]\frac{dv}{dt}[/tex]= [tex]\frac{64}{81}\pi h^2\frac{dh}{dt}[/tex]

We have;

[tex]\frac{dv}{dt}[/tex]= 548 and h = 2mm

[tex]\frac{dh}{dt} = \frac{548*81}{256\pi }[/tex]

[tex]\frac{dh}{dt}[/tex] = 55.19

           [tex]\frac{dh}{dt}[/tex] = 55.2mm per hour.

Hence, the rate in mm per hour at which the height of the water is changing when the height of the water is 2mm is 55.2

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The number of months Ben can be a member of the fitness club is 7 months .

In the question ,

it is given that Ben wants to join a fitness club ,

initial membership fees for fitness club is = $49.50

monthly fees for fitness club = $17.50

let the number of months be [tex]=[/tex] x

the total fees that Ben paid = $172

So ,according to the question

the equation to represent the situation is  

49.50 + 17.50x = 172

17.50x = 172 - 49.50

17.50x = 122.5

x = 122.5/17.50

x = 7

Therefore , Ben can be a member of fitness club for 7 months .

The given question is incomplete , the complete question is

Ben wants to join a fitness club. The fitness club charges an initial membership fee of $49.50 and a monthly fee of $17.50 , Ben has $172 to spend on a membership at the fitness club . what is the number of months ben can be a member of the fitness club ?

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Answer:

48cm = 480mm

Step-by-step explanation:

1cm = 10mm

48cm = 48 X 10 mm

48cm = 480mm

Answer:

480mm

When converting from cm to mm, multiply by 10.

48 x 10 = 480

A bit string of length 5 contains 2^5 = 32 potential values because each bit has two possible values.

The quantity of bits in a bit string determines its length. When the bit string is produced, this precise non-negative integer is fixed. The exact non-negative integers that are smaller than the bit string's length are the valid indexes. Bit strings can have zero bits or more. A series of bits is known as a bit string. Bit strings can be used to modify binary data or represent sets. In right to left order, a bit string's elements are numbered from zero to the number of bits in the string minus one.

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A vertical line passing through this point has the following equation is x=2 and A horizontal line passing through this point has the following equation is y=3.

Given that,

The point is (2,3).

We have to find the equation of the horizontal and vertical line that pass through point.

Take the point,

(2,3)

The value of x, in this example 2, will never change for a vertical line. This holds true regardless of y's value.

A vertical line passing through this point has the following equation:

x=2

The value of y, in this case 3, for a horizontal line will also never change. This holds true regardless of the value of x.

A horizontal line passing through this point has the following equation:

y=3.

Therefore, A vertical line passing through this point has the following equation is x=2 and A horizontal line passing through this point has the following equation is y=3.

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The impact of different fertilizers on crop which yields six different fertilizers have been applied to one field. here, the number of treatments in the test are 6.

Treatments are the numerous values of the factor.

The factor here is the effect of various fertilizers on crop yields.

Six different fertilizers were used.

As a result, the number of treatments equals the number of different fertilizers used = 6.

Fertilizers supply essential nutrients such as nitrogen to crops, allowing them to grow larger, faster, and produce more food. However, overfertilization can be a problem because it causes greenhouse gas emissions and eutrophication.

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42 is value of ∠JNM because ∠JNM & ∠KNL are vertically opposite angles.

What is vertically opposite angles?

∠JNM = ∠KNL

4x + 6 = 7x - 21

7x - 4x = 21 + 6

   3x = 27

   x = 27/3

   x = 9

∠JNM = 4 * 9 + 6 = 36 + 6

∠JNM =  42

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Answer:

n + 2

Step-by-step explanation:

If n is the smallest of three consecutive integers, the largest in the sequence must be only two integers greater.

Table C is the only table that represents a function

A function is a relationship between inputs where each input is related to exactly one output. Every function has a domain and codomain or range. A function is generally denoted by f(x) where x is the input

Based on the definition of function as seen above. Let's check the tables:

Table A has two inputs with the same value (4)  but with different outputs. So  Table A is not a function

Table B also has two inputs with the same value (9)  but with different outputs. Thus, Table B does not represent a function

In Table C  each input has exactly one output. Table C represents a function

Table D also has two inputs with the same value (8)  but with different outputs. So Table D does not represent a function

Therefore, Table C represents a function

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The equation, y = 3x - 15, written in standard form is 3x - y = 15

From the question, we are to write the given equation is standard form.

The given equation is

y = 3x - 15

The standard form of a linear equation is

Ax + By = C

Where A, B, and C are constants

x and y are variables

Now, we will write the given equation is the standard form of a linear equation.

y = 3x - 15

Substract y from both sides

y - y = 3x - y - 15

0 = 3x - y - 15

That is,

3x - y - 15 = 0

Add 15 to both sides of the equation

3x - y -15 + 15 = 0 + 15

3x - y = 15

Hence, the standard form is 3x - y = 15

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The area of a bull's eye is equal to: B. 452.39 mm².

The area of a circle simply refers to the region enclosed or space occupied by a circle within its boundary, and in a two-dimensional plane.

Mathematically, the area of a bull's eye can be calculated by using this formula:

Area of bull's eye = πr²

Where:

r is the radius of a circle.

Note: The radius of the bull's eye is equal to 12 mm and π = 3.14159.

Substituting the given parameters into the formula, we have;

Area of bull's eye = π × (12)²

Area of bull's eye = 3.14159 × 144

Area of bull's eye = 452.39 mm².

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Answer:

Step-by-step explanation:

We know that the area of a triangle is given by :-

Let b be the base (in feet)  of the triangle .

it is given that  , The school wants the height of the triangle to be 6 feet.

Then, the area of triangle will be :-

           (1)

The area of the logo must be at most (less than or equal to) 15 square feet.

i.e. Area ≤ 15 square feet         (2)

Now, Substitute the value of A from (1) into (2) , we get

Divide both sides by 3  , we get

Answer:

Step-by-step explanation:

all angles of a triangle add up to 180 degrees, so:

3x-40+x+60 = 180

4x = 180 - 60 + 40

4x = 160

x = 40

Check:

LS:                                    RS:

3(40)-40+40+60              180

= 180

because LS = RS,

x = 40

Hope this helps and you understand!!

Answer:

1200

Step-by-step explanation:

1,500-300=1200

I hope this helps!

42x +55y =380

The expression equivalent to (-3.3x + (-3.2)) + (5.7x + (−1) is  -3.3x + 5.7x) + ((-3.2) + (-1))

The commutative property of addition states that any change in the order of the numbers being added does not affect the sum.

a + b = b + a

The given expression is  (-3.3x + (-3.2)) + (5.7x + (−1))

on simplifying we get, -3.3x - 3.2 + 5.7x - 1 = 2.4x - 4.2

Upon checking the options provided

-3.3x + (-3.2) + 5.7x + (-1)

= 2.4x - 4.2

(-3.3x (-1)) + ((-3.2)x - 5.7)

-9 - 6.7

-3.3x + (-3.2)) + (5.7x- (-1))

2.4x - 2.2

(-3.3x + 5.7x) + ((-3.2) + (-1))

2.4x - 4.2

Therefore, the expression equivalent to (-3.3x + (-3.2)) + (5.7x + (−1) is  -3.3x + 5.7x) + ((-3.2) + (-1))

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The linear equation that represent the amount vaccine that remain is g = 61 - 0.061n. The vaccine remains in the body 24 hours after it was administered 59.536 mg. There were only 5mg of the vaccine remaining in the body after 918.033 hours.

What is rate?

A rate is a unique ratio where the two words are expressed in several units.

Given that the amount of vaccine is 61 mg.

The vaccine leaves the body at a rate of 6.1% per hour.

After 1 hour the body will consume 6.1% = 6.1/100 = 0.061 mg.

After n hour the body will consume 6.1%× n =  0.061n mg.

The remaining amount of vaccine is (61 - 0.061n).

The required linear equation that represent the remaining amount of vaccine is g = 61 - 0.061n.

Putting n =24 in the equation:

g = 61 - 0.061×24

g = 59.536 mg

The vaccine remains in the body 24 hours after it was administered 59.536 mg.

The graph represents that there were only 5mg of the vaccine remaining in the body after 918.033 hours.

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[tex]{ \qquad\qquad\huge\underline{{\sf Answer}}} [/tex]

The function shown in the graph above is a discontinuous function, at x = -2

For values of x less than -2, the left side of the graph is applicable. whose equation is :

[tex]\qquad \sf  \dashrightarrow \: y - 0 = \cfrac{1 - 0}{ - 3 - ( - 2)} (x - ( - 2))[/tex]

[tex]\qquad \sf  \dashrightarrow \: y = \cfrac{1}{ - 3 + 2} (x + 2)[/tex]

[tex]\qquad \sf  \dashrightarrow \: y = - 1(x + 2)[/tex]

[tex]\qquad \sf  \dashrightarrow \: y = - x - 2 \:\: ; \:\:x<-2[/tex]

For values of x greater than -2, the right side of the graph is applicable. whose equation is :

[tex]\qquad \sf  \dashrightarrow \: y - 4= \cfrac{4 - 2 }{0 - (-2)} (x -0)[/tex]

[tex]\qquad \sf  \dashrightarrow \: y - 4 = \cfrac{2}{2} (x)[/tex]

[tex]\qquad \sf  \dashrightarrow \: y - 4 = x[/tex]

[tex]\qquad \sf  \dashrightarrow \: y = x + 4 \: \: ;\: \: x > - 2[/tex]

So, the correct choice will be Option " A "

Answer:

[tex]\textsf{A.} \quad \begin{cases}-x -2 \quad \text{if}\;x < -2\\x + 4 \quad \;\;\;\text{if}\;x \geq -2\end{cases}[/tex]

Step-by-step explanation:

When graphing piece-wise functions:

From inspection of the given graph:

Therefore, the definition of the function is:

[tex]\begin{cases}-x + a \quad \text{if}\;x < -2\\x + 4 \quad \;\;\;\text{if}\;x \geq -2\end{cases}[/tex]

where a is some constant.

The only answer option that matches the given parameters is option A.