30 students went on a field trip to the science museum. 60% of the students tried the new Gravity Buster ride at the museum.

The Volume of largest Right Circular Cylinder that can be inscribed in Sphere of radius 3 cm is 65.3 cm³  .

Let the half height of of the cylinder be = h ;

we use h instead of [tex]\frac{h}{2}[/tex] for easier simplification ,

In order to find the Volume of cylinder , we multiply the area of  top with the total height of cylinder .

So , Volume = [tex]\pi \times (Radius Of Cylinder)^{2}\times (Height Of Cylinder)[/tex]

Volume = [tex]\pi \times (\sqrt{r^{2} -h^{2} } )^{2}\times (2h)[/tex];

Volume [tex]= 2\pi h(r^{2} -h^{2} )[/tex]

Now ,  we need the derivative of volume function and equate to 0. If we move the h inside parenthesis, we only need to use power rule to get  derivative.

So , we get , V = [tex]2\pi (r^{2} h-h^{3} )[/tex] ,

On simplifying further ,

we have ,

Volume of Largest Right Circular Cylinder  ⇒ [tex]\frac{4\sqrt{3} \pi r^{3} }{9}[/tex] ;

it is given that radius of sphere is = 3 cm ,

Substituting value of radius in Volume formula ,

we get ,

V =  [tex]\frac{4\sqrt{3} \times 3.14\times 3^{3} }{9}[/tex] ;

V = 65.2636 cm³

V ≈ 65.3 cm³.

Therefore , the volume of the largest right circular cylinder is 65.3 cm³.

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If Jason missed 3 goals and made 9 goals in one practice session the prediction we can make if the number of tries is 24 , then (c) Jason will make 18 goals .

Jason is practicing for making soccer goals and keeping a track of the results ;

the number of goals missed by Jason is = 3 goals ;

the number of goals that Jason made is = 9 goals ;

So , the total number of goals is = 12 goals ;

the ratio of making a goal to the total goals is = [tex]\frac{9}{12}[/tex] ;

So , the number of goals that Jason will make in 24 tries can be calculated as = [tex]\frac{9}{12} \times 24[/tex]

= [tex]9 \times 2[/tex]

= 18 .

Therefore , the Jason will make 18 goals in 24 tries .

The given question is incomplete , the complete question is

Jason practiced making soccer goals and kept track of the results. he missed 3 goals but made 9 in one practice session. What can Jason predict regarding goals made if his next practice session has 24 tries?

(a) Jason will make 8 goals.

(b) Jason will make 16 goals.

(c) Jason will make 18 goals.

(d) Jason will make 21 goals.

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Answer: x=(y+9)5−32 simplified

Step-by-step explanation:

Answer:

16 and 18

16 + 18 = 34 .......... .....

The options that shows expressions which are functions in the ranges they are defined are;

Option A: f(x) = 2x + 5

Option B:  f(x) = x² + 1

Real numbers are defined as the combination of rational and irrational numbers, in the number system. This means that, all the arithmetic operations can be performed on real numbers and they can be represented in the number line.

Now, integers are defined as whole numbers that can be positive, negative or zero.

a) We are told that the input of real numbers must yield only real numbers. Yes this is true because any real number we put in for x in f(x) = 2x + 5 will yield an output that is also a real number.

b) We are told that the input of real numbers must yield only real numbers. Yes this is true because any real number we put in for x in f(x) = x² + 1 will yield an output that is also a real number.

c) We are told that the input of real numbers must yield only real numbers. No this is not true because if we put -1 which is a real number for x in the denominator, we will get an undefined function.

d) We are told that the input of integers must yield only integers. No this is not true because if we put 1 for x which is an integer, we will get a fraction which is not an integer.

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Answer:

Step-by-step explanation:

6

The number of packages of 5 wheels can be made from the 30 wheels is 6.

The unitary method is a technique for solving a problem by first finding the value of a single unit, and then finding the necessary value by multiplying the single unit value.

Given that, a model car maker puts 5 wheels in each kit. A machine makes 30 wheels at a time.

Now, number of packages of 5 wheels

= 30/5

= 6

Therefore, the number of packages of 5 wheels can be made from the 30 wheels is 6.

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Answer:

x = 4

y = 28

Step-by-step explanation:

1) y = 7x

2) y = 2x + 20

substitute y = 7x into equation 2:

7x = 2x + 20   now you can solve for x:

7x - 2x = 20

5x = 20

x = 20/5 = 4

Plug x = 4 into either equation 1 or 2 to solve for y:

y = 7x = 7(4) = 28

The design has a total area of 116 cm² when measured using the area of a square.

The area is the total amount of space that an object's shape or a flat (2-D) surface occupies.

Create a square on paper by using a pencil.

Two dimensions make it up.

A shape's area on paper is the space it takes up.

Given that a square has equal sides, we can calculate its area as follows:

A = s²

The photograph below illustrates the three square-shaped pieces of fabric that Jordan used to create the design.

Find the area of each square-shaped piece of fabric and add them all up to get the total pattern area.

Inferring the area of a square, the total area would be as follows:

Total Area = 4² + 6² + 8²

Total Area = 116 cm²

Therefore, the design has a total area of 116 cm² when measured using the area of a square.

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Answer: first u have to find the perimiter for each side

Step-by-step explanation:

the answer is 100 d z

The segment partition formula is used to calculate the coordinates of a point on a line segment, given the coordinates of the two endpoints of the segment and the ratio of the desired point from the first endpoint.

The formula is:

Point = (x1 + r * (x2 - x1), y1 + r * (y2 - y1))

Where x1 and y1 are the coordinates of the first endpoint, x2 and y2 are the coordinates of the second endpoint, and r is the ratio of the desired point from the first endpoint.

The segment partition formula is used to calculate the coordinates of a point on a line segment, given the coordinates of the two endpoints and the ratio of the desired point from the first endpoint. The formula is given in the form of Point = (x1 + r * (x2 - x1), y1 + r * (y2 - y1)).

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The dimensions of the room when Alyssa's den is 8 feet longer than it is wide are 15cm as 23cm.

An equation simply means the statement that shows the relationship between the variables given. It has an equal sign to denote this.

Let the width of the den be x.

The length of the den is x+8.

We can set up the equation x*(x+8)=425 to represent the area of the den.

We can solve this equation by factoring it as x² + 8x =425.

x² + 23x - 15x - 425

x(x + 23) - 15(x + 23)

(x - 15)(x + 23)

Either way, we find that the width of the den is 15 feet and the length is 23 feet.

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value of x = 8 as per logarithm laws.

In mathematics, logarithm is an exponent or power for which a particular number is raised to achieve a required number. In other words, logarithm is a mathematical expression that states about how many times a number can be multiplied by the same number to get some required numbers.

The method of expressing any exponential relationship in the inverse form is called log notation.

In this question, we are given a log base 2 or binary logarithm.

given, ㏒₂ x = 3

     as per the logarithm laws ㏒a y = m

                                          y = a∧m

                               we write. ㏒₂ x = 3

                                                  x = 2³

                            hence, x = 8

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Answer: yes, it uses the Associative Property

Step-by-step explanation:

Answer:

(-3, -2)

Step-by-step explanation:

Notice how the lines intersect? that exact point is the solution.

When 70% of families will have four-wheelers and 30% of families will have two-wheelers, the projected guest attendance is 3000+1200 = 4200.

In mathematics, a percentage is a number or ratio that is expressed as a fraction of 100. Occasionally, the acronyms "pct.," "pct," and "pc" are also used. But it is commonly indicated by the percent sign, "%." The % amount has no dimensions. Percentages are essentially fractions when the denominator is 100. Use the percent sign (%) to indicate that a number is a percentage by placing it next to it. For instance, you score a 75% if you properly answer 75 out of 100 questions on a test (75/100). Divide the money by the total and multiply the result by 100 to calculate percentages. The formula for calculating the percentage is (value/total) x 100%.

given

2500 guests are present when four-wheelers are available.

two wheelers, the number of guests is 1500,

making the total 2500 + 1500 = 4000.

70 percent of families will own four-wheelers, or 3000/4000/100.

30% of families will own two-wheelers, which equals 4000/100 * 30%, or 1200.

When 70% of families will have four-wheelers and 30% of families will have two-wheelers, the projected guest attendance is 3000+1200 = 4200.

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When you log an e, you are essentially taking the natural logarithm of the number. This means that you are taking the logarithm of a number to the base e, which is about 2.718. The result of this calculation is the number of times the number must be multiplied by itself to get the original number.

For example, if you were to log an e, it would be equal to 1, since e x e = e. If you log a number bigger than e, such as 8, the result would be equal to 2.079, which means that 8 must be multiplied by itself twice (2.079 times) to get the original 8.

In general, when you log a number, you can think of it as a way of seeing how many times that number needs to be multiplied by itself to get the original number. This can be useful in many fields, from mathematics to engineering to physics, to find the mathematical relationship between two numbers.

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No, 4, 8 and 10 cannot be the sides of a right triangle. So 4, 8 and 10 does not make a right triangle.

In a right triangle, the side opposite the right angle (the hypotenuse) is the longest side. The side opposite the 90-degree angle is the hypotenuse and it follows the Pythagorean theorem which states that the square of the hypotenuse is equal to the sum of the squares of the legs, so:

c² = a² + b²

In this case, c = 10, a = 8 and b = 4,

so 8² + 4² = 64 + 16 = 80 ≠ 10²

That is it does not follows the theorem. Therefore, 4, 8 and 10 cannot be the sides of a right triangle.

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We want to find an equation and the sixth term of the given geometric sequence.

The equation is: [tex]a_{n} = 4*a_{n}-1[/tex] and the sixth term is equal to 512

In a geometric sequence, each term is a constant times the previous term, so the general relation is:

[tex]a_{n} = k*a_{n}-1[/tex]

Here we can use any pair of consecutive terms to find the value of the constant, for example, if we use the first two, we have:

[tex]8 = k*2\\8/2 = 4 = k[/tex]

Now we know the value of the constant, then the general formula is: [tex]a_{n} = 4*a_{n}-1[/tex]

Now we can use this to get the sixth term:

[tex]a_{6} = 4*a_{5}-1=4*128 = 512[/tex]

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The solution of the system of equations y =0 x=4

To solve the system of equations, we must set the two equations equal to each other and solve for x.

y = -2x + 8

y = x - 4

We start by subtracting the second equation from the first equation.

-2x + 8 = (x - 4)

We then add 4 to both sides of the equation.

-2x + 12 = x

We then subtract 12 from both sides of the equation.

-3x = -12

Finally, we divide both sides of the equation by -3.

x = 4

Now that we have solved for x, we can substitute 6 for x in either equation and solve for y.

y = -2(4) + 8

y = -8 + 8

y = 0

Therefore, the solution of the system of equations is (4, 0).

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What is the solution of the system of equations  y= -2x + 8 and y = x - 4?

A (A) histogram is a useful tool for condensing qualitative data.

An effective tool for summarizing qualitative data is a histogram.

The distribution of numerical data is roughly depicted by a histogram.

Karl Pearson was the person who first coined the phrase.  

The first stage in creating a histogram is to "bin" (or "bucket") the range of values, divide it into a series of intervals, and then count the number of values that fall into each interval.

The bins are often defined as a series of discrete intervals that don't overlap.

The bins (intervals) must be close together and frequently, though not always, have the same size.

Therefore, a (A) histogram is a useful tool for condensing qualitative data.

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Correct option is B, The three zeros are 2, 3, -3.

The zeros of a function are the values of its variables that meet the equation and result in the function's value being equal to 0. The zeros of a function can be represented graphically as the x-coordinates (or x-intercepts) where the graph intersects the x-axis.

If a number's unit digit or end indicates a zero, it is a multiple of 10 and so divisible by 10. As a result, the amount of zeros at the end of every number determines how many times it may be raised to the power of 10.

y= (x-2)(x-3)(x+3)

The zeros of the above function are -

x = 2

x = 3

x = -3

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Gary, Mary, and Rory have 96 candies altogether.

Let's assume that the original number of candies that Gary, Mary, and Rory had is "x".

After Gary gives Mary half of all his candies, he would have x/2 candies.

Then, after Mary gives Rory half of all the candies she has at the moment, she would have x/4 candies.

And then, after Rory gives Gary half of all the candies he (Rory) has at the moment, he would have x/8 candies.

Now, we know that Gary would have 12 more candies than he had originally, which means:

x/2 + x/8 = x/2 + x/4 - 12

We can combine like terms and simplify the equation:

x/2 + x/8 = x/4 + x/4 - 12

x/8 = 12

x = 8 * 12

x = 96

Thus, Gary, Mary, and Rory have 96 candies altogether.

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The percent error in the amount of water Rich added is 15.93%.

When compared to the actual value, the percent error is the difference between the estimated and actual values.

The difference between the estimated value and the actual value in relation to the actual value is given as a percentage and is known as the percent error. In other words, the relative error times 100 equals the percent error.

Given that Rich added water to a solution in science class is 26.2 milliliters

Whereas the directions said to add water is 22.6 milliliters

The amount of water that is added more is 26.2 -22.6 = 3.6 milliliters

The percent error is = (3.6/22.6)*100%

The percent error is = 15.9292*100%

Therefore, the correct answer is option b) 15.93%.

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Answer:

The common difference is 4.

Step-by-step explanation:

Answer:

∠ SQT = 63°

Step-by-step explanation:

since QS bisects ∠ RQT , then

∠ RQS = ∠ SQT = 7x + 7

then

∠ RQS + ∠ SQT = ∠ RQT , that is

7x + 7 + 7x + 7 = 9x + 54

14x + 14 = 9x + 54 ( subtract 9x from both sides )

5x + 14 = 54 ( subtract 14 from both sides )

5x = 40 ( divide both sides by 5 )

x = 8

Then

∠ SQT = 7x + 7 = 7(8) + 7 = 56 + 7 = 63°

The cost of a pack of gum bought by Lionel is $2.1.

Let the variable g represent the cost of a pack of gum.

Let the variable c represent the cost of a candy bar.

Since Lionel bought 4 candy bars and 2 packs of gum at the gas station and spent $9.80, a linear equation that models this situation is;

4c + 2g = 9.80    ......equation (1)

Additionally, two packs of gum cost the same as three candy bars:

2g = 3c     ......equation (2)

c = 2g/3     ......equation (3)

Substituting equation (3) in equation (1), we get:

4(2g/3) + 2g = 9.80

8g/3 + 2g = 9.80

14g/3 = 9.80

14g = 29.4

= 29.4/14

= $2.1

The cost of a pack of gum is $2.1.

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The complete question is -

Lionel bought 4 candy bars and 2 packs of gum at the gas station and spent $9.80. Two packs of gum cost the same as three candy bars. Let g represent the cost of a pack of gum and c represent the cost of a candy bar. What is the cost of a pack of gum?

The given expression (s⁻⁵)³ is equivalent to (1/s)¹⁵.

Exponent is a quantity representing the power to which a given number or expression is to be raised, usually expressed as a raised symbol beside the number or expression. Mathematically -

[tex]$b^x = \underbrace{b \times \dots \times b}_{x \text{ times}}[/tex]

where -

[b] = base of the logarithm

[x] = exponent

Given is the expression as follows -

(s⁻⁵)³

We can write the expression as -

(s⁻⁵)³ = (1/s⁵)³ = (1/s¹⁵) = (1/s)¹⁵

Therefore, the given expression (s⁻⁵)³ is equivalent to (1/s)¹⁵.

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