The cylinder shown here has a height of 7 centimeters and a radius of 4 centimeters.
1. What is the area of the base of the cylinder? Express your answer in terms of .
2. How many cubic centimeters of fluid can fill this cylinder? Express your answer in terms of .
3. Give a decimal approximation of your answer to the second question using 3.14 to approximate n.

Answer: 135

Step-by-step explanation:

Counting by 5 The last point at the end of the box and whisker plot is 135

Answer:

1)10abc^2+6a^2bc

2)6.6x^2yz-2.8xy^2z+0.5xyz^2

Step-by-step explanation:

Answer:

nth term = n²-6

Step-by-step explanation:

we know our nth-term formula is going to be of the form an² + bn + c. We just have to find a, b, and c.

In this series,

-5, -2, 3, 10, 19....

a=1, b=0, c=-6

nth term = n²-6

if n=1 then,

nth term=1²-6

⇒nth term=-5

The values and graph of the equation 3x - 2y = 6 is attached below while the slope is 3/2

The equation of a straight line can be represented in various forms. One of the most commonly used forms is the point-slope form, which is represented as:

y - y1 = m (x - x1)

where (x1, y1) is a point on the line, and m is the slope of the line, which is the rate of change of y with respect to x.

Another common form of the equation of a line is the slope-intercept form, which is represented as:

y = mx + b

where m is the slope of the line, and b is the y-intercept, which is the point where the line crosses the y-axis.

In this problem, we need to write the table of values and the find the slope of the line.

3x - 2y = 6

rewriting this equation;

2y = 3x - 6

y = 3x/2 - 3

when y = 0

0 = 3x/2 - 3

3x/2 = 3

3x = 2 * 3

3x = 6

x = 2

when x = 0

y = 3(0)/2 - 3

y = 0 - 3

y = -3

The slope of the line can be calculated using the two points from above.

slope (m) = y₂ - y₁ / x₂ - x₁

m = -3 - 0 / 0 - 2

m = 3/2

The slope is 3/2

The graph of the equation is attached below

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The tables/graphs with their equations are

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

Tables, Graphs and equations

Table (a)

Here, we notice that:

The output is the 5 less than three times the input

This is represented as

y = 3x - 5

Table (b)

Here, we notice that:

The output is the 2 more than negative 12 times the input

This is represented as

y = -12x + 2

Graph (c)

Here, we have the following points

(4, 0) and (0, -5)

A linear function is represented as

y = mx + c

Where

c = y when x = 0

So, we have

y = mx - 5

Using the other point, we have

0 = 4m - 5

This gives

m = 5/4

So, we have

y = 5/4x - 5

Graph (d)

Here, we have the following points

(0.5, 0) and (0, 3)

A linear function is represented as

y = mx + c

Where

c = y when x = 0

So, we have

y = mx + 3

Using the other point, we have

0 = 0.5m + 3

This gives

m = -6

So, we have

y = -6x + 3

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Answer:

[tex]\mbox{\large $0.5 + 0.16 \bar {3}$ = \boxed{\dfrac{199}{300}}}[/tex]

Step-by-step explanation:

[tex]0.16\bar{3} = 0.16333333333\\[/tex]

the 3 repeats until infinity

Let's multiply this by 100 to move the non-repeating part to the left of the decimal point

0.1633333333...... x 100 = 16.333333333333333...

.333333 = 1/3

Therefore the recurring number multiplied by 100 is
[tex]16 + \dfrac{1}{3} = \dfrac{16 \times 3 + 1}{3}=\dfrac{49}{3}[/tex]

Since this fraction was arrived at by multiplying by 100, divide this fraction by 100 to get back the fraction in its original decimal value of 0.163333

[tex]\dfrac{49}{3} \div 100[/tex]

To divide by a number, multiply by the reciprocal of that number

Reciprocal of 100 is 1/100:

[tex]\dfrac{49}{3} \div 100 = \dfrac{49}{3} \times \dfrac{1}{100} = \dfrac{49}{300}[/tex]

(You can verify this by dividing 49 by 300 in a calculator and seeing that the result is 0.163333333333333333333 i.e. 0.16333 recurring

We want to add 0.5 to this.

0.5 = [tex]\dfrac{1}{2}[/tex]

so
0.5 + 0.16333333 = 0.6633333

[tex]= \dfrac{1}{2} + \dfrac{49}{300}[/tex]

We can write [tex]\dfrac{1}{2}[/tex] as [tex]\dfrac{150}{300}[/tex]  by multiplying numerator and denominator by 150

So we get

[tex]0.5 + 0.1633333 = \dfrac{150}{300} + \dfrac{49}{300} = \dfrac{150+49}{300} = \dfrac{199}{300}[/tex]

If you perform this division on a calculator you will get the answer as 0.663333 = [tex]0.66\bar{3}[/tex] which is what you get when you add 0.5 and [tex]0.16\bar{3}[/tex]

Answer:

Step-by-step explanation:

Greetings!!!

The given two numbers ratio.

[tex] \frac{5}{4} [/tex]

The smaller number is 32

[tex] \frac{5}{4} \times 32[/tex]

convert elements into fraction

[tex] \frac{5}{4} \times \frac{32}{1} [/tex]

Apply fraction rule

[tex] \frac{a}{b} \times \frac{c}{d} = \frac{a \times c}{b \times d} [/tex]

Multiply the numbers

[tex] \frac{5 \times 32}{4 \times 1} [/tex]

Divide the numbers

[tex] \frac{32}{8} = 8 \\ 8 \times 5 = 40[/tex]

Hope it helps!!!

Answer:

(24) + (20) + (8) = 52 ft^2

Step-by-step explanation:

This figure is a compound of 3 rectangles that can be split up like in my attached picture.

The top, horizontal rectangle is 8x3 = 24 sq ft.

The bottom, almost square rectangle is 4x5 = 20 sq ft.

The middle rectangle has a height of 4 feet and a width of (8-6) = 2 feet.

So, its area is 4x2= 8 sq ft.

The compound figure is the sum of all of these areas:

24 + 20 + 8 = 52

The area of the compound figure is 52 sq ft.

Area of 1 = 8 * 3 = 24

Area of 2 = 4 * 2 = 8

Area of 3 = 5 * 4 = 20

Total area = 24 + 8 + 20 = 52

The expression that is equivalent to 5^6 is A.125 x 125

Index forms are defined as mathematical forms of writing numbers that are too large or small in more convenient forms.

Other terms for index forms are called standard forms or scientific notations.

They are also described as numbers or variables that are raised to an exponent.

From the information given, we have that;

5⁶

This is replicating 5 in 6 places, we have the representation as;

5 × 5 × 5 × 5 × 5 × 5

Hence, the expression is 125 x 125

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The complete question:

A baker uses the equation y = 12x to predict the revenue generated from selling a cakes. She uses equation y= 450 +4.5x to

model the cost to produce a cakes:

What does (60, 720), the solution of the system -450 +4.5x &

y=12x represent?

Solution:-

The solution of the system (-450 + 4.5x, y = 12x) at (60, 720) represents :

a. The point where the revenue generated from selling 60 cakes is 720 dollars

b. The cost to produce those 60 cakes is 720 dollars.

In geometry, A system of equations is a collection of two or more equations with the same set of unknown variables. In solving a system of equations, we try to calculate values for each of the unknowns that will satisfy each and every equation in the system.

The given system of equations is:

y = 12x (equation 1)

y = 450 + 4.5x (equation 2)

where x represents the number of cakes produced and sold, y represents the revenue generated from selling x cakes, and 450 + 4.5x represents the cost to produce x cakes.

To find the solution of the system, we can substitute equation 1 into equation 2, and solve for x as follows:

12x = 450 + 4.5x

7.5x = 450

x = 60

Substituting this value of x into equation 1 gives us:

y = 12(60)

y = 720

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Answer:

(X-3)5=575

5x-15=575

5x=575+15

5x=590

X= 590:5

X= 118

Answer: 37 points

Step-by-step explanation:

Answer:

x + 3y = 9

Step-by-step explanation:

The expected number of aces in a poker hand given that the first card drawn is an ace is 0.235.

If the first card drawn is an ace, then there are only 3 aces left in the deck of 51 cards from which to draw the remaining 4 cards. Therefore, we can model the number of aces in the poker hand as a binomial random variable with parameters n = 4 (the number of cards after the first ace) and p = 3/51 (the probability of drawing an ace from the remaining deck).

The expected number of aces in a poker hand given that the first card drawn is an ace can be calculated as follows:

E(X) = np = 4 * 3/51 = 12/51 = 0.235

Therefore, the expected number of aces in a poker hand given that the first card drawn is an ace is approximately 0.235.

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____ The given question is incorrect, the correct question is given below:

A poker hand consists of five cards drawn from a standard 52-card deck. find the expected number of aces in a poker hand given that the first card drawn is an ace.

first one is a

Step-by-step explanation:

By applying the slope of the function at that point, linear approximation provides an estimate of the value of a function close to a beginning point.

When estimating the value of a function at a nearby location, linear approximation uses the slope of the function at a particular position. In order to arrive at the starting position, it first calculates the difference between the two points, multiplies it by the slope, and adds it. This provides a rough estimate of the function's value at the new location. A technique for calculating a function's value close to a beginning point is called linear approximation. It is predicated on the notion that a linear function can be used to roughly approximate the function close to the point of interest. This indicates that the value of the function at surrounding places can be inferred from the slope of the function at the point in question.

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Answer: The two shaded parts of the wall have a combined area of 20m * 12m + 16m * 15m = 240 + 240 = 480 square meters.

Therefore, the volume of yellow paint required is 480 * 0.1 = 48 litres.

Step-by-step explanation:

Answer:

Y < (1/3) x - 5

Answer:

Answer is Below ------v

1. clockwise

2. 3

1. (y, -x)

2. (3x,3y)

Answer:

6

Step-by-step explanation:

12 is the full length. point E marks 1/2 of the line. 12-6=6

if it's asking the length of d-e, then the answer is (6) because the entire length of line is twelve and in the top line e-f in 6 and 6-12=6

The ratio tables based on the information will be:

12 16

3 4

36 48

Ratio in Mathematics simply demonstrates how many times one number can be able to fit into another number. It should be noted that ratios contrast two numbers by dividing them. In this case, A/B will be the formula if one is comparing one variable (A) to another variable (B).

This simply indicates that you're dividing the variable A by B. Let us say for instance, the ratio will be 3/10 if A is 3 and B is 10.

Since the ratio is 3:4. When the smaller number is 36, the larger number will be:

= 4/3 × 36.

= 48

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The side of the triangle from shortest to longest can be arranged as,

A triangle is a polygon with three sides such that the sum of all the interior angles is always 180°.

In a triangle, the side opposite to the biggest angle is always the lengthiest, while the side opposite to the smallest angle is the shortest.
Given that the measure of ∠A is 100°, therefore, the length of the side BC will be the lengthiest.
Also, the measure of ∠B is 20°, therefore, the length of the side AC will be the shortest.

Hence, BC > AB > AC.

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There are 5,760 ways to arrange the books on the bookshelf.

A permutation is an ordered arrangement of objects, and it can be calculated as follows:

ⁿPₓ = n! / (n - x)!

where n is the total number of objects and r is the number of objects that we are arranging.

To determine the total number of ways in which we can arrange the books on a bookshelf, we need to first calculate the total number of possible arrangements. We can do this by using the fundamental principle of counting, which tells us that the total number of possible arrangements is equal to the product of the number of ways in which each book can be arranged.

Therefore, the total number of possible arrangements can be calculated as follows:

Total number of possible arrangements = Number of ways to arrange math books × Number of ways to arrange history books × Number of ways to arrange science books

In our case, we have 4 math books, 5 history books, and 2 science books, so we can calculate the number of permutations for each type of book as follows:

Number of ways to arrange math books = ⁴P₄ = 4! / (4-4)! = 4! / 0! = 24

Number of ways to arrange history books = ⁵P₅ = 5! / (5-5)! = 5! / 0! = 120

Number of ways to arrange science books = ²P₂ = 2! / (2-2)! = 2! / 0! = 2

Now, we can substitute these values in the formula for the total number of possible arrangements:

Total number of possible arrangements = 24 × 120 × 2 = 5,760

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A statement which best describes the graph of y ≥ -x² + 8x - 2 include the following: B. The vertex is at (4, 14). The parabola is a solid line that opens down. Shading is above the parabola.

Generally speaking, the graph of a quadratic function would always form a parabolic curve because it is a u-shaped. For this quadratic function, we can logically deduce that the graph is a downward parabola because the coefficient of x² is negative and the value of "a" is less than zero (0).

By critically observing the graph of the given quadratic function, we can logically deduce that the solutions (roots) and vertex are as follows;

x = 0.258, y = 0.

x = 7.742, y = 0.

Vertex = (4, 14).

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Answer:

-5x-96/12

Step-by-step explanation:

Firstly we want ot combine the multiplied terms into one fraction:

(1x/3-3)+(-3/4 x-5)

Then we multiply by 1:

(x/3-3)+(-3/4 x-5)

Find common denominator:

(x/3+3(-3)/3)+(-3/4 x-5)

Combine fractions with common denominator:

(x+3(-3)/3)+(-3/4 x-5)

Multiply the numbers:

(x-9/3)+(-3/4 x-5)

Combine multiplied terms into a single fraction:

x-9/3+(-3x/4 -5)

Find common denominator:

x-9/3+(-3x/4 + 4(-5)/4)

Combine fractions with common denominator:

x-9/3+(-3x + 4(-5)/4)

Multiply the numbers:

x-9/3 + (-3x-20/4)

Find common denominator:

4(x-9)/12 + 3(-3x-20)/20

Combine fractions with common denominator:

4(x-9)+3(-3x-20)/12

Distribute:

4x-36+3(-3x-20)/12

Distribute:

4x-36-9x-60/12

Subtract the numbers:

4x - 96 - 9x/12

Combine like terms:

-5x - 96/12

Answer: -5x-96/12

Answer:

x = 4 twice.

Step-by-step explanation:

x^2-8x+ 16=0

Bring the constant to the other side.

x^2-8x=-16

Half the coefficient of x and square the result. Add to both sides.

x^2-8x+[-8/2]^2=-16+(-8/2)^2

x^2-8x+16= 16-16

x^2-8x+16=0

Now, whenever there's a perfect square constant, take the root of that constant. Since the coeff. of x is negative (-8),

(x-4)(x-4)=0  [-4^2=16 and -4+(-4)=-8]

Therefore, x-4=0 twice.

x=4 twice.

Hope this helps!  :]

Answer: The length is 9 units and the width is 1 unit

Step-by-step explanation:

We can use the formula for the area of a rectangle to solve this problem. The formula is A = l * w, where A is the area, l is the length, and w is the width.

We have A = 9, and we know that w = l - 8. Substituting this into the formula, we get:

9 = l * (l - 8)

We can rearrange this to solve for l:

9 = l^2 - 8l

Adding 8l to both sides of the equation, we get:

9 + 8l = l^2

Subtracting 9 from both sides, we get:

8l = l^2 - 9

We can factor this to get:

l(l - 9) = 0

Since the product of two numbers is zero only when one of them is zero, we can set each factor equal to zero and solve:

l = 0 or l - 9 = 0

Adding 9 to both sides of the second equation, we get:

l = 9

Therefore, the length of the rectangle is 9 units.

Answer:

2.3333 inches

Step-by-step explanation:

To find the appropriate scale factor, we need to determine how many times smaller the piece of paper is compared to the dog. We can start by finding the ratio of the length of the paper to the length of the dog:

3 inches / 9 inches = 1/3

Similarly, the ratio of the width of the paper to the height of the dog is:

5 inches / 7 inches = 5/7

So, the smaller of these two ratios, 1/3, is the appropriate scale factor for Meredith to use in her drawing. This means that the length of the dog in the drawing will be 9 inches * 1/3 = 3 inches, and the height will be 7 inches * 1/3 = 2.3333 inches.

Given point D is the centroid of triangle ABC, BD = 4x + 2 and DF = 3x and the value of x is -1

Centroid is a term used in triangles and it is equals to the reciprocal of three-second of the distance from each midpoint of the given triangle to each vertices.

Given point D is the centroid of triangle ABC, BD = 4x + 2 and DF = 3x and Centroid is a term used in triangles and it is equals to the reciprocal of three-second of the distance from each midpoint of the given triangle to each vertices.

we know that,

BD = 4x+2

DF = 3x

So by the given formulae, we used to solve the x value as,

BD = (1/(3/2)) [DF]

BD = (2/3)[DF]

4x+2 = (2/3)(3x)

4x+2 = 2(x)

4x+2 = 2x

4x-2x = -2

2x = -2

x = -1

Therefore, the value of x is x = -1

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