A right circular cylinder has the dimensions shown below.

r = 17.2 yd
h = 45.3 yd

What is the volume of the cylinder? Use 3.14 for π.

Round to the nearest tenth and include correct units.

Show all your work.

Option (b) "3/4 to the power of 2 - 6/16" is the expression that is  equivalent to 3/16.

A formula is a set of two or more numbers or variables and one or more mathematical operations. This mathematical operation is addition, subtraction, multiplication, or division. The formula has the following structure:

The expression is (number/variable, arithmetic operator, number/variable).

Solution according to the given information:

Given, x = 3/4

Option(a): 2x+1/16 = (2×3/4) +1/16

                              = 3/2 + 1/16

                              =25/16

Which is not equal to 3/16

Option(b): (3/4)² - 6/16 = 9/16 - 6/16 = 3/16

Which is equivalent to 3/16

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The option E. (3/2, - 1/2, - 3) is not a solution to the system of linear equations.

The system of linear equations given is:

3x + y + z = 1
2x + y - 4z = 2

The answer that is not a solution to this system is option. To check this, we can substitute (3/2, - 1/2, - 3) into the system and solve:
3*(3/2) + (-1/2) + (-3) = 1
2*(3/2) + (-1/2) - 4*(-3) = 2

After simplifying, we get 9/2 - 1/2 + 9/2 ≠ 1 and 9 - 1 - 12 ≠ 2, so option E. (3/2, - 1/2, - 3) is not a solution to the system of linear equations.

A system of equations is a set of two or more equations in which we will find unknowns.

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The scale unit that James used to create scale drawing of school library is 1 inch = 6 feet.

A measurement scale used to represent actual dimensions in a model or drawing. Scales include units of measurement such as inches, feet, and meters, scale unit. A scale used to represent actual dimensions on a drawing or map. 

A scale map is a two-dimensional representation of a real-world object or place. Maps and floor plans are examples of scale drawings. The scale shows what the length on the scale drawing represents in actual length .

According to the question:

Given, 78 feet length of library is represented by 13 inch

Let, "x" be the number of feet that 1 inch represents.

∴ 13x = 78 feet

  ⇒x = 78/13

  ⇒x = 6

So, 1 inch equals 6 feet.

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Answer:

the answer would be 1 inch = 6 feet

Step-by-step explanation:

What is scale unit?

A measurement scale used to represent actual dimensions in a model or drawing. Scales include units of measurement such as inches, feet, and meters, scale unit. A scale used to represent actual dimensions on a drawing or map.

What is scale drawing?

A scale map is a two-dimensional representation of a real-world object or place. Maps and floor plans are examples of scale drawings. The scale shows what the length on the scale drawing represents in actual length .

Solution:

Given, 78 feet length of library is represented by 13 inch

Let, "x" be the number of feet that 1 inch represents.

∴ 13x = 78 feet

 ⇒x = 78/13

 ⇒x = 6

So, 1 inch equals 6 feet.

(the new location) of point under each of the following general transformations are as follows:

a. Image: (3, -10)

b. Image: (-1, -10)

c. Image: (-4/3, -10)

d. Image: (14/3, -10)

What is general transformations?

A transformation is a procedure that involves either changing an object's orientation to create an image or expanding or reducing its size to create a new one.

We'll use the given point (4, -10) as the input for each transformation, and apply the transformation to find the new location of the point.

a. f(x) = (x + 2) - 3

f(4) = (4 + 2) - 3 = 3

Therefore, the new location of the point under the transformation f(x) = (x + 2) - 3 is (3, -10).

b. f(x) = 2(x - 4) - 1

f(4) = 2(4 - 4) - 1 = -1

Therefore, the new location of the point under the transformation f(x) = 2(x - 4) - 1 is (-1, -10).

c. f(x) = -1/3x

f(4) = -1/3(4) = -4/3

Therefore, the new location of the point under the transformation f(x) = -1/3x is (-4/3, -10).

d. f(x) = (2/3)x + 2

f(4) = (2/3)(4) + 2 = 8/3 + 2 = 14/3

Therefore, the new location of the point under the transformation f(x) = (2/3)x + 2 is (14/3, -10).

In each case, the image of the point is the new location after applying the transformation.

a. Image: (3, -10)

b. Image: (-1, -10)

c. Image: (-4/3, -10)

d. Image: (14/3, -10)

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a) 6% of 34 is 2.04
b) 17 is 50% of 34

c) 18 is 30% of 60

d) 7% of 49 is 3.43.

a. To find 6% of 34, you can multiply 34 by 0.06 (which is the decimal equivalent of 6%): 34 * 0.06 = 2.04. So 6% of 34 is 2.04.

b. To find what percent 17 is of 34, you can divide 17 by 34 and then multiply by 100 to convert the decimal to a percentage: (17/34) * 100 = 50%. So 17 is 50% of 34.

c. To find what number 18 is 30% of, you can divide 18 by 0.30 (which is the decimal equivalent of 30%): 18 / 0.30 = 60. So 18 is 30% of 60.

d. To find 7% of 49, you can multiply 49 by 0.07 (which is the decimal equivalent of 7%): 49 * 0.07 = 3.43. So 7% of 49 is 3.43.

8. Unfortunately, I cannot see the number line that you are referring to, so I cannot provide an answer for this part of the question.

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81-100. ------2

1-20----------2

21-40---------4

41-60----------1

61-80----------1

The mass of the chemicals being propelled is 0.41 kilograms.

The correct answer is: 0.41 kilograms.

To find the mass of the chemicals being propelled, we can use the formula for momentum:

momentum = mass x velocity

Since the momentum of the cracker before it is launched is zero, and the momentum after it is launched is the sum of the momentum of the cracker and the momentum of the chemicals, we can set up an equation:

0 = (1.5 kg)(15 m/s) + (mass of chemicals)(55 m/s)

Next, we can rearrange the equation to solve for the mass of the chemicals:

(mass of chemicals)(55 m/s) = -(1.5 kg)(15 m/s)

mass of chemicals = -(1.5 kg)(15 m/s) / (55 m/s)

mass of chemicals = -22.5 kg / 55 m/s

mass of chemicals = -0.41 kg

So the mass of the chemicals being propelled is 0.41 kilograms.

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The cοst fοr οne οf each item is:

Candle: $1.625

Licοrice stick: $0.975

Candy: $2.50

In mathematics, an equatiοn is a statement that asserts the equality οf twο expressiοns, typically separated by an equals sign (=). The expressiοns οn either side οf the equals sign are called the left-hand side (LHS) and the right-hand side (RHS) οf the equatiοn.

Let's use variables tο represent the cοst οf each item. Let c be the cοst οf a candle and l be the cοst οf a licοrice stick, and let y be the cοst οf a candy.

Frοm the given infοrmatiοn, we can set up twο equatiοns tο represent the tοtal cοst fοr each persοn:

2c + l = 3.25 (Equatiοn 1)

y + 4l = 2.50 (Equatiοn 2)

We can then sοlve fοr each variable by using algebraic manipulatiοn.

Frοm Equatiοn 1, we can isοlate l by subtracting 2c frοm bοth sides:

l = 3.25 - 2c

We can substitute this expressiοn fοr l intο Equatiοn 2, and sοlve fοr y:

y + 4(3.25 - 2c) = 2.50

y + 13 - 8c = 2.50

y = 2.50 - 13 + 8c

y = 8c - 10.5

Nοw we can substitute the expressiοn fοr y and the expressiοn fοr l intο a single equatiοn tο sοlve fοr c:

2c + (8c - 10.5) = 3.25 + 2.5

10c - 10.5 = 5.75

10c = 16.25

c = 1.625

Sο a candle cοsts $1.625. We can use this value tο find the cοst οf a licοrice stick:

l = 3.25 - 2c

l = 3.25 - 2(1.625)

l = 0.975

Sο a licοrice stick cοsts $0.975. Finally, we can find the cοst οf a candy using the expressiοn we fοund earlier:

y = 8c - 10.5

y = 8(1.625) - 10.5

y = 2.5

Sο a candy cοsts $2.50.

Therefοre, the cοst fοr οne οf each item is:

Candle: $1.625

Licοrice stick: $0.975

Candy: $2.50

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The standard equation of this ellipse is x²/144 + y²/80 = 1.

The standard equation of an ellipse is (x-h)²/a² + (y-k)²/b² = 1, where (h,k) is the center of the ellipse, a is the semi-major axis, and b is the semi-minor axis.

In this case, the center of the ellipse is (0,0) since the vertices and foci are both on the y-axis. The distance between the vertices is 24 (12 - (-12)), so the semi-major axis is 12. The distance between the foci is 16 (8 - (-8)), so the distance between the center and each focus is 8. Using the formula c² = a² - b², where c is the distance between the center and each focus, we can solve for b:

c² = a² - b²
8² = 12² - b²
64 = 144 - b²
b² = 80

So the equation of the ellipse is (x-0)²/12² + (y-0)²/80 = 1, or x²/144 + y²/80 = 1.

You keep getting (x²)/80 + (y²)/144 because you are switching the values of a and b. The semi-major axis should be in the denominator of the x term, and the semi-minor axis should be in the denominator of the y term.

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Answer: A: 20,40,120

Step-by-step explanation:

Angle A is smaller than Angle B as it is less than 1 time as big as it.

The list of angles from smallest to largest is C, A, and B.

120 x (1/3) = 40

20 < 40

Hope this helps!

Answer:

hi

Step-by-step explanation:

this is the answer

hope this helps

good luck;)

Answer: We can write the piecewise defined function for the monthly cost C(x) as follows:

C(x) =

45.75 - 9.55, if x ≤ 500

45.75 - 9.55 + 0.35(x - 500), if x > 500

Explanation:

For the first 500 minutes, the monthly cost is a flat rate of $45.75 for the plan fee and $9.55 for taxes, so the total cost is simply the sum of these two amounts: C(x) = 45.75 + 9.55 = 55.30, for x ≤ 500.

For any additional minutes beyond the 500-min limit, there is an additional charge of $0.35 per minute, so the cost increases linearly with the number of extra minutes used. The expression (x - 500) represents the number of minutes beyond the limit, so we multiply this by the rate of $0.35 per minute and add this amount to the base cost of $55.30, giving the piecewise expression:

C(x) =

55.30, if x ≤ 500

55.30 + 0.35(x - 500), if x > 500

Therefore, the piecewise defined function for the monthly cost C(x) is:

C(x) =

45.75 - 9.55, if x ≤ 500

45.75 - 9.55 + 0.35(x - 500), if x > 500

Note: The two expressions are equivalent, but the second expression is simplified by combining the constants.

Step-by-step explanation:

It is not possible to use Cramer's Rule to solve the system of equations you provided. This is because Cramer's Rule can only be applied to systems of linear equations that have the same number of equations as there are unknowns.

In the system you provided, there are four equations but only two unknowns. This means that Cramer's Rule cannot be applied.

Instead, you can use other methods such as substitution or elimination to solve the system. However, it is important to note that with more equations than unknowns, it is possible that there may be no solution or an infinite number of solutions.

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Answer:

-2

Step-by-step explanation:

[tex]m=\frac{4-(-8)}{-4-2} \\m=\frac{4+(+8)}{-4-2} \\m=\frac{12}{-6} \\m=\frac{2}{-1} \\m=-2[/tex]

∆ABC = ∆BCD because they are congruent

If two sides and the included angle of one triangle are equal to the corresponding sides and angle of another triangle, the triangles are congruent.

AB is parallel to CD and AB is equal to CD,

Therefore AC = BD( opposite sides of a parallelogram are equal

therefore CB is common to both triangle

We can therefore say that all the corresponding three sides of the two triangles are equal

i.e AC = BD

AB = CD

CB = CB

therefore triangle ABC and BCD are congruent

This means ;

∆ABC = ∆BCD

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Answer:

see explanation

Step-by-step explanation:

the sum of the 3 angles in a triangle = 180°

sum the 3 angles and equate to 180

4x + 21 + x - 10 + 2x + 8 = 180

7x + 19 = 180 ( subtract 19 from both sides )

7x = 161 ( divide both sides by 7 )

x = 23

Then angles in triangle are

4x + 21 = 4(23) + 21 = 92 + 21 = 113°

x - 10 = 23 - 10 = 13°

7x + 8 = 7(23) + 8 = 161 + 8 = 169°

the only 2 possible angle measures are A and E

The probability that the selected marble is red is 0

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

Number of marbles = 10

Blue = 3

Yellow = 7

Using the above as a guide, we have the following:

P(Red) = Number of red/Number of marbles

Substitute the known values in the above equation, so, we have the following representation

P(Red) = 0/10

Evaluate

P(Red) = 0

Hence, the probability is 0

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[tex]\boxed{sin^{2}x + cos^{2}x = 1}[/tex]

a) [tex]cos^{2}x = 1 - sin^{2}x[/tex]

b) [tex]3sin^{2}x - 4cos^{2}x = 3sin^{2}x - 4(1 - sin^{2}x) = \\[/tex]

[tex]= 3sin^{2}x - 4 + 4sin^{2}x = 7sin^{2}x - 4[/tex]

Answer:

1. [tex]75[/tex]

2. [tex]4x^{8}[/tex]

3. [tex]128[/tex]

Step-by-step explanation:

[tex]\frac{3*5^9}{5^7}=\frac{3*5^2*5^7}{5^7}=3*5^2=75[/tex]

[tex]\sqrt{16x^{16}}=4\sqrt{x^{16}} =4x^8[/tex]

[tex]\frac{(-5)(2^8)}{-6+1}/2=\frac{(-5)(2^8)}{(-5)(2)}=\frac{2^8}{2}=2^7=128[/tex]

A) The probability of at least one red ball being obtained is 1 - the probability of no red balls being obtained.

The probability of no red balls being obtained is (7/17)*(6/16)*(5/15)*(4/14)*(3/13) = 0.0096. Therefore, the probability of at least one red ball being obtained is 1 - 0.0096 = 0.9904.

B) The probability of two red balls and three black balls being obtained is (10/17)*(9/16)*(7/15)*(6/14)*(5/13) = 0.0909. The probability of one red ball and four black balls being obtained is (10/17)*(7/16)*(6/15)*(5/14)*(4/13) = 0.0216.
C) The probability of getting k red balls and (5-k) black balls is (10 choose k)*(7 choose (5-k))/(17 choose 5). This can be calculated for each value of k from 0 to 5 and summed to find the total probability.

For example, when k=0, the probability is (10 choose 0)*(7 choose 5)/(17 choose 5) = 0.0096. When k=1, the probability is (10 choose 1)*(7 choose 4)/(17 choose 5) = 0.0909. The total probability is the sum of these individual probabilities.

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a. The polyhedron that can be constructed using the net made of squares is a cube.

b. The polyhedron that can be constructed using the net made of squares is also a cube.

c. The polyhedron that can be constructed using the net made of a regular hexagon and isosceles triangles is a hexagonal pyramid.

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a) The probability of rolling a Yahtzee is 0.00077

b) The probability of rolling either a small straight or a large straight is 0.1389

Given data:

(a)

To calculate the probability of rolling a Yahtzee on the first round, we need to determine how many outcomes correspond to a Yahtzee and divide it by the total number of possible outcomes when rolling five dice.

A Yahtzee occurs when all five dice show the same number. There are 6 possible outcomes (each number from 1 to 6), and each outcome has only 1 way of occurring. So, there are 6 ways to roll a Yahtzee.

The total number of possible outcomes when rolling five dice is 6^5 (since each die has 6 sides).

Probability of rolling a Yahtzee = (Number of Yahtzee outcomes) / (Total number of outcomes)

[tex]= \frac{6} {6^5}[/tex]

≈ 0.00077 (rounded to 5 decimal places)

(b)

In the second round, you have (2, 3, 4, 6, 6). In the third round, you choose to re-roll both sixes.

A small straight is when you have four consecutive numbers among the dice (e.g., 1, 2, 3, 4, or 2, 3, 4, 5, or 3, 4, 5, 6).

There are three possible small straights: (2, 3, 4, 5), (3, 4, 5, 6), and (1, 2, 3, 4). Each of these outcomes has only one way of occurring.

A large straight is when all five dice are in a row (e.g., 1, 2, 3, 4, 5 or 2, 3, 4, 5, 6).

There are two possible large straights: (1, 2, 3, 4, 5) and (2, 3, 4, 5, 6). Each of these outcomes has only one way of occurring.

Total favorable outcomes (small straights + large straights) = 3 + 2 = 5

Total number of possible outcomes when re-rolling two dice = 6^2 = 36

Probability of rolling either a small straight or a large straight = (Number of favorable outcomes) / (Total number of outcomes)

[tex]=\frac{5}{36}[/tex]

≈ 0.1389 (rounded to 4 decimal places)

Hence, the probability that you roll either a small straight or a large straight after re-rolling the dice is approximately 0.1389.

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The cost of admission for a group of 5 people is $200 dollars.

The cost of admission for a group of 5 people is given by the function C(p) = 40p, where p is the number of people in the group. To find the cost for a group of 5 people, we simply plug in 5 for p and solve for C:

C(5) = 40(5)
C(5) = 200

Therefore, the cost of admission for a group of 5 people is $200 dollars.

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Answer:

Step-by-step explanation:

[tex]\angle 2,\angle AEG, \angle GEB[/tex]

Answer:

Step-by-step explanation:

f(x)=x^4−x^2+9

Because it only covers those who are entering the sports centre, the survey will be prejudiced.

This means that the survey will only reflect the opinions of those who are likely to have positive perceptions of the sports facilities and who are interested in using them. It does not include the viewpoints of those who do not use or hold a poor opinion of the sporting facilities.

Those who don't use the facilities, for instance, could have bad perceptions of the sports centre if it is renowned for being pricey or challenging to get to. The survey will miss important information if it simply polls visitors to the sports centre.

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The algebraic equation "4x = 22.2 - 1.9" could be used to find the price of one tire patch.

Mathematical equations with one or more variables and algebraic operations like addition, subtraction, multiplication, division, exponentiation, and roots are known as algebraic equations. By identifying the values of the unknown variables that fulfill the equation, these equations can be used to illustrate mathematical connections between variables and to solve issues.

Although algebraic equations can take many different forms, they often require utilizing the equal sign (=) to make one expression equal to another. For instance, the algebraic equation x + 2 = 7 shows the connection between the constants 2 and 7 and the unknown variable x.

The equation that could be used to find the price of one tire patch is:

4x = 22.2 - 1.9

This equation represents the total cost of the four tire patches (4x) subtracted from the initial balance on Rhyan's gift card ($22.20) and the remaining balance after the sale ($1.90).

Simplifying the equation, we get:

4x = 20.3

Dividing both sides by 4, we get:

x = 5.075

So the price of one tire patch is $5.075.

Therefore, the equation "4x = 22.2 - 1.9" could be used to find the price of one tire patch. None of the other equations listed would lead to the correct answer.

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Answer:

yo

Step-by-step explanation:

C and E

The sum of these probabilities is 1, the mean number of runs per inning is 0.46, and the standard deviation of this probability distribution is 0.839.

The sum of these probabilities is simply the sum of the values in the table:

EP(x) = 0.74 + 0.12 + 0.07 + 0.04 + 0.03 = 1

The mean number of runs per inning can be calculated using the formula for the expected value of a discrete random variable:

E(x) = ∑xP(x) = (0)(0.74) + (1)(0.12) + (2)(0.07) + (3)(0.04) + (4)(0.03) = 0.46

The standard deviation of this probability distribution can be calculated using the formula for the standard deviation of a discrete random variable:

σ = √[∑(x - E(x))^2P(x)]

=> √[(0 - 0.46)^2(0.74) + (1 - 0.46)^2(0.12) + (2 - 0.46)^2(0.07) + (3 - 0.46)^2(0.04) + (4 - 0.46)^2(0.03)]

=> 0.839
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Answer:

10

Step-by-step explanation:

27-[tex]3x^{3}[/tex]+(4 x [tex]2x^{2}[/tex]) - 6

= 27 - 27 + (4 x 4) - 6

= 0 + 16 - 6

= 10

Answer: 10

Step-by-step explanation:

27 - 3^3 + 4 × 2^2 - 6

= 27 - 27 + 4 × 4 - 6 (since 3^3 = 27 and 2^2 = 4)

= 0 + 16 - 6= 10

Therefore, the simplified value of the expression is 10.