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1. Rupert is copying some files from his computer to a compact disc, like
the one shown above.If the diameter of the compact disc is 120
millimeters, what is the approximate area ignoring the center hole? (Use.
3.14 for pi) *

Answer:

The answer selected is correct

Step-by-step explanation:

Answers to be filled are rectangle, \(2\pi\) , equal, \(2\pi r^2\).

Given,

In the question:

Suppose the bottom surface, or base, of a cylinder is divided into 16 congruent sectors. then the sectors are rearranged as shown.

Open this GeoGebra activity to divide the circle into even more sectors and rearrange the sectors for yourself.

To complete the statement to compare the areas of the two figures and find the area of the base of the cylinder.

Now, According to the question:

To complete the statements

A circle of radius 'r' and rearranged figure out of sectors of the same circle.

When the sectors of the circle are rearranged , they are close to forming a rectangle with a length of 2\(\pi\)r units and a width of r units.

The area of the rearranged figure is equal to that of the circle. So, the area of the circular base 2\(\pi r^2\) sq. units

Hence, Answers to be filled are rectangle, \(2\pi\) , equal, \(2\pi r^2\).

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When the sectors of the circle are rearranged, they are close to forming a

rectangle with a length of 2*pi*r units and a width of r units. The area of the rearranged figure is equal to that of the circle. So, the area of the circular base 2*pi*r square units.

Answer:

Step-by-step explanation:

I am sorry but please give detailed question

Answer: Hoops Haven

Step-by-step explanation:

Answer:

3x + 15 = 3*10 + 15 = 30 + 15 = 45

3x + 15 = 45

Now,

2x + 25 = 2*10 + 25 = 20 + 25 = 45

2x + 25 = 45

Step-by-step explanation:

3x + 15 + 2x + 25 = 90

or, 5x + 40 = 90

or, 5x = 90 - 40

so, 5x = 50

so, x = 50/5 = 10

Given, A= (1,0,1) be a point in R and let P be the plane in R3 with equation \(z+y+3z=−7\). We need to find a point B lies on the plane P and produces a vector AB that is orthogonal to P.

The equation of the plane P is given as y + z = -7. By putting z = 0, we get y = -7. By putting y = 0, we get z = -7.

Let\(B = (2, 1, 4) and C = (0, -7, 0)\).

To find the vector AB, we subtract the coordinates of point A (0, -7, 0) from B:

\(AB = (2 - 0, 1 - (-7), 4 - 0) = (2, 8, 4).\)

The normal vector of plane P can be represented as n = (a, b, c) since it is orthogonal to the plane.

Using the equation of the plane, we have: \(a*0 + b*(-7) + c*0 = 0\)

This simplifies to -7b = 0, which gives us b = 0.

To find the values of a and c, we can take any non-zero vector that is orthogonal to AB. Let's choose a = 1 and c = -1.

So, the normal vector n = (1, 0, -1).

Now, let's find the projection of the vector AC onto n. The projection can be calculated using the dot product:

\(CD = AC dot n / |n|^2 * n\\AC = (2 - 0, 1 - (-7), 4 - 0) = (2, 8, 4)\)

Calculating the dot product:

\(AC dot n = (2, 8, 4) dot (1, 0, -1) = 2*1 + 8*0 + 4*(-1) = 2 - 4 = -2\\|n|^2 = 1^2 + 0^2 + (-1)^2 = 1 + 0 + 1 = 2\\CD = (-2 / 2) * (1, 0, -1) = (-1, 0, 1)\)

Finally, the point D on the plane P can be found by adding the coordinates of C and CD:

\(D = (0, -7, 0) + (-1, 0, 1) = (-1, -7, 1).\)

Hence, the correct option is B = (2, 1, 4).

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B = (2,1,4) point B lies on the plane P and produces a vector AB that is orthogonal to P. The correct answer is Option B.

Given, A= (1,0,1) be a point in R and let P be the plane in R3 with equation . We need to find a point B lies on the plane P and produces a vector AB that is orthogonal to P.

The equation of the plane P is given as y + z = -7.

By putting z = 0, we get y = -7. By putting y = 0, we get z = -7.

To find the vector AB, we subtract the coordinates of point A (0, -7, 0) from B:

The normal vector of plane P can be represented as n = (a, b, c) since it is orthogonal to the plane.

Using the equation of the plane, we have:

This simplifies to -7b = 0, which gives us b = 0.

To find the values of a and c, we can take any non-zero vector that is orthogonal to AB. Let's choose a = 1 and c = -1.

So, the normal vector n = (1, 0, -1).

Now, let's find the projection of the vector AC onto n. The projection can be calculated using the dot product:

Calculating the dot product:

Finally, the point D on the plane P can be found by adding the coordinates of C and CD:

Hence, the correct option is B = (2, 1, 4).

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The superposition of cos 16t and cos 12t is 2 sin 14t sin 2t, while the superposition of cos 6t and cos 4t is 2 sin 5t sin t. Furthermore, the superposition of cos 8t and cos 6t can be expressed as 2 cos t cos 7t, and the superposition of sin 18t and sin 12t can be written as 2 cos 3t sin 15t.

The superposition of trigonometric functions as a product can be written as follows:

a. The superposition of cos 16t and cos 12t can be expressed as the product of two terms: 2 sin 14t sin 2t. This is derived using the identity cos α - cos β = -2 sin ((α+β)/2) sin ((α-β)/2).

b. The superposition of cos 6t and cos 4t can be written as the product of two terms: 2 sin 5t sin t. This is obtained using the identity cos α - cos β = -2 sin ((α+β)/2) sin ((α-β)/2).

c. The superposition of cos 8t and cos 6t can be represented as the product of two terms: 2 cos t cos 7t. This is derived using the identity cos α + cos β = 2 cos ((α+β)/2) cos ((α-β)/2).

d. The superposition of sin 18t and sin 12t can be expressed as the product of two terms: 2 cos 3t sin 15t. This is obtained using the identity sin α + sin β = 2 cos ((α-β)/2) sin ((α+β)/2).

In each case, we can simplify the superposition of trigonometric functions into a product of two terms using appropriate trigonometric identities. This form allows us to analyze the combined behavior of the functions and gain insights into their periodicity, phase shifts, and amplitudes.

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Answer:

x=5

Step-by-step explanation:

We know that a pentagon is in total 540 degrees. From this, we add all other numbers and set them equal to 540 to solve for x.

So, after adding all the angles and setting them equal to 540, we get this.

21x+435=540

21x=105

x= 5

If you want, plug 5 into x and see if it adds up to 540 to check

21(5)+435=540

The p-value is established and hypotheses are accepted or rejected based on these results, the result is significant.

The general recurrence of z-scores empowers us to decide a few things in regards to the comparing crude scores, except for deciding qualities concerning goodness or disagreeableness. The number of standard deviations a given data point has from the population mean is measured using Z-scores. In statistics, particularly normal distribution, these are frequently used to normalize data and evaluate a data point's position for improved data analysis. One of the purposes of the general recurrence of z-scores is that it permits us to work out the likelihood of an occasion happening in a standard typical conveyance.

Using mathematical software or a standard normal table, the probability distribution for z-scores can be found and used to calculate the probabilities of occurrences below, above, or between two z-scores. The general recurrence of z-scores is additionally utilized in deciding whether a noticed contrast is impressive and measurably critical. By determining whether the difference is significant if the corresponding z-score falls outside the range of 1.96, this can be accomplished. Since the p-value is established and hypotheses are accepted or rejected based on these results, the result is significant.

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Step-by-step explanation:

Let x be the amount invested at 6% so that 18000-x is the amount invested at 7.5% both in dollars.

The total interest in 3 years is $3330 so we can write: 0.06x(3)+0.075(18000-x)(3)=3330

Solve for x:

0.06x(3)+0.075(18000−x)(3)=3330

Step 1: Simplify both sides of the equation.

0.06x(3)+0.075(18000−x)(3)=3330

0.06x(3)+−0.225x+4050=3330(Distribute)

0.18x+−0.225x+4050=3330

(0.18x+−0.225x)+(4050)=3330(Combine Like Terms)

−0.045x+4050=3330

−0.045x+4050=3330

Step 2: Subtract 4050 from both sides.

−0.045x+4050−4050=3330−4050

−0.045x=−720

Step 3: Divide both sides by -0.045.

−0.045x/−0.045=−720/−0.045

x=16000

x=16000

So, the amounts borrowed are:

Bank at 6% = 16000

Bank at 7.5% = 2000

Answer:

The answer to your problem is, 156

First lets find out how many feet or in one yard ?

Well 1 yard = 3 feet.

Now that we know that we can use our knowledge to answer the next question:

If Bill ran 52 yards, how many feet did he ran?

We can do math to solve our answer. :

1 x 52 = 52.

Now we need to multiply 52 x 3.

That is a little bit to much, so lets make the problem easier!

By breaking up the problem \/ to make it more easier.

50 x 3. ( 5 x 3 = 15, just add a zero! ) = 150

3 x 2 = 6.

Next add:

150 + 6 = 156.

Thus the answer to your problem is, 156

The two come separately, and the p(wed.) value for each one is 0.0841. It is founded on likelihood on probability.

Probability is a way to gauge how likely something is to happen. Many things are hard to predict with complete certainty. We can only forecast how likely an event is to occur using it, or how likely it is to occur.

The probability is typically defined as the proportion of positive outcomes to all outcomes in the sample space. Probability of an event P(E) = (Number of favourable outcomes) is how it is stated (Sample space).

based on the facts provided;

p(0) = p(w,w)

= 0.29² = 0.0841

p(1) = p(t, w+t) + p(w, t)

= 2p(w,t) +p(t,t) = 2·.29·.37 + .37² = 0.3515

p(2) = p(f, w+t+f) +p(w+t, f)

= 0.16(2(.29+.37)+.16) = 0.2368

p(3) = p(s, w+t+f+s) +p(w+t+f, s)

= 0.18(2(.29+.37+.16) +.18) = 0.3276

In summary, your pmf is ...

y : p(y)

0 : 0.0841

1 : 0.3515

2 : 0.2368

3 : 0.3276

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Answer:

Step-by-step explanation:

Domain: [-4,-2,0,2,4]

Range: [2,4,6,8,10]

Step-by-step explanation:

Stan seventeen and stream rock with you

The probability that at least 1 ball was red, given that the first ball was replaced before the second draw is 28.5%; and the probability that at least 1 ball was red, given that the first ball was not replaced before the second draw is 22.5%.

To find the probability that at least 1 ball was​ red, given that the first ball was replaced before the second draw. Not replaced before the second draw:

Therefore, the probability that at least 1 ball was red, given that the first ball was replaced before the second draw is 28.5%; and the probability that at least 1 ball was red, given that the first ball was not replaced before the second draw is 22.5%.

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The complete question is given below:

Two balls are drawn in succession out of a box containing 2 red and 5 white balls. Find the probability that at least 1 ball was​ red, given that the first ball was (Upper A )Replaced before the second draw. (Upper B )Not replaced before the second draw.

Answer:

\( {x}^{2} = {(13 - 6)}^{2} + {9}^{2} = {7 }^{2} + {9}^{2} \\ = 130 \\ x = \sqrt{130} = 11.4\)

\(\sf\green{The\:circumference\:of\:the\:circle\:is \:25.1428\:cm.}\)

\(\sf\purple{Radius\:of\:the\:circle}\) = 4 cm.

\(\sf\red{The\:circumference\:of\:the\:circle.}\)

We know that,

\(\sf\purple{Circumference\:of\:a\:circle}\) =

\(2 \: \pi \: r \\ = 2 \times \frac{22}{7} \times 4 \: cm\\ = \frac{176}{7} \: cm \\ = 25.1428 \: cm\)

\({\boxed{\mathcal{\red{Hence,\:the\:circumference\:of\:the\:circle\:is\:25.1428\:cm.}}}}\)

\(\circ \: \: { \underline{ \boxed{ \sf{ \color{green}{Happy\:learning.}}}}}∘\)

Answer:

A)  4 cats

Step-by-step explanation:

let x = 16-y

substitute to get:

18(16-y) + 30y = 432

288 - 18y + 30y = 432

12y = 144

y = 12

x = 4

The functions 7 are inverse functions while the functions 8 are not inverse functions

To verify that f and g are inverse functions, we need to show that:

Let's apply these conditions to the given functions:

f(x) = 5x + 2; g(x) = (x−2)/5

f(g(x)) = f((x−2)/5) = 5((x−2)/5) + 2 = x − 2 + 2 = x

g(f(x)) = g(5x + 2) = ((5x + 2) − 2)/5 = 5x/5 = x

Since f(g(x)) = x and g(f(x)) = x, we can conclude that f and g are inverse functions.

f(x) = ½x − 7; g(x) = 2x + 14

f(g(x)) = f(2x + 14) = ½(2x + 14) − 7 = x

g(f(x)) = g(½x − 7) = 2(½x − 7) + 14 = x − 7 + 14 = x + 7

Since f(g(x)) = x and g(f(x)) ≠ x, we can conclude that f and g are not inverse functions.

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The exact value of the surface area of the solid formed when the graph of r = 2cos(θ), where 0 ≤ θ ≤ π/2, is revolved about the polar axis is π [cos(4) - 1].

find the surface area of the solid formed when the graph of r = 2cos(θ), where 0 ≤ θ ≤ π/2, is revolved about the polar axis, we can use the formula for surface area in polar coordinates:

S.A. = 2π ∫[α, β] r sin(θ) √(r^2 + (dr/dθ)^2) dθ

In this case, we have r = 2cos(θ) and dr/dθ = -2sin(θ).

Substituting these values into the surface area formula, we get:

S.A. = 2π ∫[α, β] (2cos(θ))sin(θ) √((2cos(θ))^2 + (-2sin(θ))^2) dθ

   = 2π ∫[α, β] 2cos(θ)sin(θ) √(4cos^2(θ) + 4sin^2(θ)) dθ

   = 2π ∫[α, β] 2cos(θ)sin(θ) √(4(cos^2(θ) + sin^2(θ))) dθ

   = 2π ∫[α, β] 2cos(θ)sin(θ) √(4) dθ

   = 4π ∫[α, β] cos(θ)sin(θ) dθ

To evaluate this integral, we can use a trigonometric identity: cos(θ)sin(θ) = (1/2)sin(2θ). Then, the integral becomes:

S.A. = 4π ∫[α, β] (1/2)sin(2θ) dθ

   = 2π ∫[α, β] sin(2θ) dθ

   = 2π [-cos(2θ)/2] [α, β]

   = π [cos(2α) - cos(2β)]

Now, we need to find the values of α and β that correspond to the given range of θ, which is 0 ≤ θ ≤ π/2.

When θ = 0, r = 2cos(0) = 2, so α = 2.

When θ = π/2, r = 2cos(π/2) = 0, so β = 0.

Substituting these values into the surface area formula, we get:

S.A. = π [cos(2(2)) - cos(2(0))]

   = π [cos(4) - cos(0)]

  = π [cos(4) - 1]

Therefore, the exact value of the surface area of the solid formed when the graph of r = 2cos(θ), where 0 ≤ θ ≤ π/2, is revolved about the polar axis is π [cos(4) - 1].

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Answer:

1) (x - 9)(x + 2)  ==> trinomials

2) (s + z) (3m - 2n)  ==> factorising by parts

3) (x + 2)(5x + 3)  ==> factorising with a leading coefficient

4) 9y²(3y² - 2)  ==> GCF

5) (4m - 12)(4m + 12)  ==> DoPS

Step-by-step explanation:

1). Find multiples of -18 that add up to -7

Multiples of -18 : (only one number can be negative, because positive*negative = negative)

1, 18 or 3, 6 or 2, 9

Only one pair adds up to -7 which is -9 + 2

Hence ==> (x - 9)(x + 2)

2). Find the common things between the terms and factorise it out  

3m(s + z) - 2n(s + z)

Since the terms inside the brackets are the same, you simplify it to:

(s + z) (3m - 2n)

3). Multiply the first coefficient with the last coefficient: 5(6) = 30

Find two numbers that multiply to 30 and add up to the middle coefficient -13.

Multiples of 30 are: 1, 30 or 2, 15 or 3, 10 or 5,6, but only one pair would add to -13 and that is 3 and 10

So the next step is to write it in this form: 5x² + 10x + 3x + 6

Factorise: 5x(x + 2) + 3(x + 2)

(x + 2)(5x + 3)

4). Find the greatest common factor within 27y⁴ and 18y², which is 9y²

9y²(3y² - 2)

5). Square root each number: √16 = 4 and √144 = 12

(4m - 12)(4m + 12)

Answer:

5

Step-by-step explanation:

=>(x+5)/y

=>(20+5)/5

=>25/5

=>5

Answer:

5

Step-by-step explanation:

plug in x 20+5=25

plug in y =5

25/5=5

The power of -1 to a function, or \(((f^{-1})(x)),\)represents the inverse function of f. In other words, if f(x) produces a certain output y, then the inverse function\(f^{-1}(y)\)will produce the input x. It is important to note that not all functions have an inverse, and if they do, they may only be valid for certain inputs and outputs.

In mathematics, the inverse function of a function f (also called the inverse of f) is a function that undoes the operation of f1. The inverse of f exists if and only if f is bijective.

\(((f^{-1})(x)),\)

The inverse function of f is denoted by. For a function, its inverse admits an explicit description: it sends each element to the unique element such that f(x) = y1.

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Answer:

1= 41

2=85

3= 95

4=85

5= 36

6= 49

7= 188

Step-by-step explanation:

I think that's the answer

Answer:

0.96 inches

Step-by-step explanation:

The first step is to find the diameter given the circumference. This is the formula for circumference:

\(C=\pi d\)

In terms of d, the formula looks like this:

\(d=\frac{C}{\pi}\)

For the softball, the diameter is approximately:

\(d=\frac{12}{\pi} =3.82\)

For the baseball:

\(d=\frac{9}{\pi } =2.86\)

Find the difference:

\(3.82-2.86=0.96\)

The approximate difference in diameters is 0.96 inches!

Answer: 0.96 inches

Step-by-step explanation:

Answer:39.9

Step-by-step explanation:1 kilogram is 0.453592 kilograms so if you multiply that number by 88 you will get 39.9

Given parameters:

Table of values

Planets                       Average distance from Sun(miles)

Mars                                                 1.42 x 10⁸

Pluto                                                 3.67 x 10⁹

The average distance from Earth to Sun is 93.08 x 10⁶ miles

   So:

            1 Astronomical unit = 93.08 x 10⁶ miles

Unknown;

Distance in Astronomical unit of Mars and Pluto.

                 Since :

                 93.08 x 10⁶ miles   =  1 Au

For Mars;

                 1.42 x 10⁸ miles  =   \(\frac{1.42 x 10^{8} miles x 1Au}{93.08 x 10^{6} miles }\)

                                             = 0.015 x 10²AU

                                             = 1.5AU

For Pluto:

                93.08 x 10⁶ miles   =  1 Au

                 3.67 x 10⁹ miles  = \(\frac{3.67 x 10^{9} miles x 1Au}{93.08 x 10^{6} miles }\)

                                              = 0.039428 x 10³AU

                                              = 39.428AU

               To the nearest tenth = 39.4AU

So the distance of Mars in AU is 1.5AU and Pluto is 39.4AU

The marked angles in Fig. 13.25 are 96 degrees and 72 degrees.

In Fig. 13.25, we have two parallel lines AB and CD. We also have a transversal XY that intersects these two parallel lines. We need to find the marked angles, which are 4x and 3x.

Step 1: Identify the pairs of corresponding angles.

The corresponding angles are the ones that are on the same side of the transversal and in the same position with respect to the parallel lines.

The corresponding angles are equal. For example, angle AXY and angle CYX are corresponding angles and are equal. Similarly, angle BYX and angle DXY are corresponding angles and are equal. We can write the corresponding angles as follows: Angle AXY = angle CYXAngle BYX = angle DXYStep 2:Identify the pairs of alternate interior angles.

The alternate interior angles are the ones that are on opposite sides of the transversal and in the same position with respect to the parallel lines.

The alternate interior angles are equal. For example, angle BXY and angle CXD are alternate interior angles and are equal. Similarly, angle AYX and angle DYC are alternate interior angles and are equal. We can write the alternate interior angles as follows:

Angle BXY = angle CXDAngle AYX = angle DYCStep 3:Identify the pair of interior angles on the same side of the transversal. The interior angles on the same side of the transversal are supplementary. That is, their sum is 180 degrees.

For example, angle AXY and angle BYX are interior angles on the same side of the transversal, and their sum is 180 degrees. We can write this as follows: Angle AXY + angle BYX = 180Step 4:Use the relationships we have identified to solve for x.

We can start by using the relationship between angle BXY and angle CXD, which are alternate interior angles. We have angle BXY = angle CXD4x = 3x + 10x = 10Next, we can use the relationship between angle AXY and angle BYX, which are interior angles on the same side of the transversal.

We have:angle AXY + angle BYX = 180(3x + 10) + 4x = 1807x + 10 = 1807x = 170x = 24Finally, we can substitute x = 24 into the expressions for 4x and 3x to find the marked angles. We have:4x = 4(24) = 963x = 3(24) = 72Therefore, the marked angles in Fig. 13.25 are 96 degrees and 72 degrees.

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The equation that would help the mathematician model the surface area of a square piece of paper as it was repeatedly cut is \(y = 36 \times \frac{1}{2}^x\)

Option D is the correct answer.

We have,

In this equation, the variable x represents the number of times the square is cut in half, and y represents the surface area of the square.

As x increases, the exponent of 1/2 decreases, causing the value of y to decrease.

This exponential decay accurately represents the idea that the surface area becomes less and less but never reaches zero units²

Thus,

The equation that would help the mathematician model the surface area of a square piece of paper as it was repeatedly cut is \(y = 36 \times \frac{1}{2}^x\).

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The correct equation that would help model the surface area of a square piece of paper as it is repeatedly cut in half is:  \(\(y=36(\frac{1}{2})^x\)\)

As the square is cut in half, the side length of the square is divided by 2, resulting in the area being divided by \(\(2^2 = 4\)\).

Therefore, the equation \(y=36(\frac{1}{2})^x\)\)accurately represents the decreasing surface area of the square as it is repeatedly cut in half.

and, \(\(y=x^2+4x-16\)\)is a quadratic equation that does not represent the decreasing nature of the surface area.

and, \(\(y=-25x^2\)\) is a quadratic equation with a negative coefficient.

and, \(\(y=9(2)^x\)\)represents exponential growth rather than the decreasing nature of the surface area when the square is cut in half.

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Answer:

Step-by-step explanation:

1.) 700*0.42 = 294. Out of the 700 people at the concert, 294 are tennagers.

2.) 1.07*$450 = $481.50, including sales tax (final price)

3.) 120/(100%-85%) = 120/0.15 = 800. Original amount of water is 800 ml (Check by 800mL*0.15, which equals 120 mL)

4.) 100-35-45 = 20%

250*20% = 50; Out of the 250 sandwiches, Josh made 50 ham sandwiches.