Find the volume of this cylinder. Round your answer to the nearest tenth.

Answer:

The answer is A.

Answer:

Step 2

Step-by-step explanation:

In step 1, Gary had the right idea of multiplying both sides by 4 to eliminate the denominator, but in step 2, Gary makes a mistake since e should equal 10 not 8. 2.5 * 4 = 10 not 8

Answer:

B) Step 2

Step-by-step explanation:

Gary's mistake occurs in Step 2. He was right to multiply both sides of the equation by 4 to find e, but his error is in the multiplication of 2.5*4. 2.5*4 = 10, not 8.

Answer:

\(\orange{\rule{40pt}{555555pt}} \green{\rule{40pt}{555555pt}} \blue{\rule{40pt}{555555pt}} \red{\rule{40pt}{555555pt}}\pink{\rule{40pt}{555555pt}}\yellow{\rule{40pt}{555555pt}}\)

Reflect over the y axis; dilate by a scale factor of 2.

==================================================

Explanation:

Let's focus on the bottom-most points of each rhombus. For rhombus A on the left, that point in question is (-3,1). For rhombus B, that corresponding lowest point is (6,2).

If we were to reflect rhombus A over the y axis, then (-3,1) would move to (3,1). Simply swap the sign of the x coordinate while keeping the y coordinate the same. Now compare (3,1) to (6,2). Notice that we can multiply each coordinate of (3,1) by the scale factor 2 so that we jump to (6,2)

\((3,1) \stackrel{\text{mult by 2}}{\longrightarrow} (6,2)\)

This "multiply by 2" operation is done to each point of the reflected blue rhombus so that we end up with the green rhombus after all is said and done. Also, this trick of multiplying the coordinates by the scale factor only works if the center of dilation is the origin.

In short, we do two things:

which allows us to go from blue (rhombus A) to green (rhombus B)

Answer:

45

Step-by-step explanation:

The constant of proportionality is 45

The SinL as a fraction in the simplest form is 12/13.

We are given

The side NM = 5,

The side LM = 12,

By using Pythagoras' theorem, we can say that;

NL² = NM² + LM²

Substitute the values of NM and LM;

NL² = 12² + 5²

NL = 13,

For Sin L = perpendicular side/hypotenuse side

Sin L = NM / NL,

Sin L = 12/13

Therefore, the SinL as a fraction in the simplest form is 12/13

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The  quotient of 302 ÷ (9.1 x \(10^4)\) in scientific notation is approximately 3.31868131868 x \(10^1\)

Dividing 302 by 9.1 gives:

302 ÷ 9.1 ≈ 33.1868131868

Now, to express this result in scientific notation, we need to move the decimal point to the appropriate position to create a number between 1 and 10. In this case, we move the decimal point two places to the left:

33.1868131868 ≈ 3.31868131868 x\(10^1\)

Therefore, the quotient of 302 ÷ (9.1 x \(10^4\)) in scientific notation is approximately 3.31868131868 x\(10^1\)

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Answer:

Please check the explanation.

Step-by-step explanation:

We know that a function is a relation where each input or x-value of the X set has a unique y-value or output of the Y set.

In other words, we can not have duplicated inputs as there should be only 1 output for each input.

Let us create the table from the given mapping

x                  y

2                20

2                40

4                40

3                30

From the table, it is clear that the input x = 2 is repeated twice. In other words, the input x = 2 is duplicated.

As we know that we can not have duplicated inputs as there should be only 1 output for each input.

Therefore, the given relation/mapping DOES NOT represent a function.

Determining the domain of a relation:

We know that the domain of the relation is the set of all the x-coordinates of the given points or ordered pairs.

Thus, the domain of the relation in ascending order is:

Domain D = {2, 3, 4}

Determining the range of a relation:

We know that the range of the relation is the set of all the y-coordinates of the given points or ordered pairs.

Thus, the range of the relation in ascending order is:

Domain D = {20, 30, 40}

Answer:

1 : 8

Step-by-step explanation:

Answer:

$8 per hour

Step-by-step explanation:

First you have to do 16/2 or 32/4 to get your answer which is 8

Hope this helps!

Step-by-step explanation:

slope of given line:

m=2

as lines are parallel so slopes will be equal:

required slope m=2

By using point slope form:

y-y1=m(x-x1)

y-5=2(x-5)

y-5=2x-10

y=2x-10+5

y=2x-5

Note:if you need to ask any question please let me know.

Answer:

1/4; 0.4; 0.55; 3/5

0.25, 0.40, 0.55, 0.60

Already in order.

0.4; 1/4; 0.55; 3/5

0.40, 0.25, 0.55, 0.60

1/4; 0.4; 0.55; 3/5

1/4; 3/5; 0.4; 0.55

0.25, 0.60, 0.40, 0.55

1/4; 0.4; 0.55; 3/5

3/5; 0.4; 1/4; 0.55

0.60, 0.40, 0.25, 0.55

1/4; 0.4; 0.55; 3/5

Answer:

Step-by-step explanation:

8*4 1/3= 34 2/3 or 34.6

Answer:

1)  695.3 m²

2)  8 ft

3)  172.0 in²

Step-by-step explanation:

To find the area of a regular polygon, we can use the following formula:

\(\boxed{\begin{minipage}{5.5cm}\underline{Area of a regular polygon}\\\\$A=\dfrac{s^2n}{4 \tan\left(\dfrac{180^{\circ}}{n}\right)}$\\\\\\where:\\\phantom{ww}$\bullet$ $n$ is the number of sides.\\ \phantom{ww}$\bullet$ $s$ is the side length.\\\end{minipage}}\)

Given the polygon is an octagon, n = 8.

Given each side measures 12 m, s = 12.

Substitute the values of n and s into the formula for area and solve for A:

\(\implies A=\dfrac{(12)^2 \cdot 8}{4 \tan\left(\dfrac{180^{\circ}}{8}\right)}\)

\(\implies A=\dfrac{144 \cdot 8}{4 \tan\left(22.5^{\circ}\right)}\)

\(\implies A=\dfrac{1152}{4 \tan\left(22.5^{\circ}\right)}\)

\(\implies A=\dfrac{288}{\tan\left(22.5^{\circ}\right)}\)

\(\implies A=695.29350...\)

Therefore, the area of a regular octagon with side length 12 m is 695.3 m² rounded to the nearest tenth.

\(\hrulefill\)

The sum of an interior angle of a regular polygon and its corresponding exterior angle is always 180°.

If the exterior angle of a polygon measures 40°, then its interior angle measures 140°.

To determine the number of sides of the regular polygon given its interior angle, we can use this formula, where n is the number of sides:

\(\boxed{\textsf{Interior angle of a regular polygon} = \dfrac{180^{\circ}(n-2)}{n}}\)

Therefore:

\(\implies 140^{\circ}=\dfrac{180^{\circ}(n-2)}{n}\)

\(\implies 140^{\circ}n=180^{\circ}n - 360^{\circ}\)

\(\implies 40^{\circ}n=360^{\circ}\)

\(\implies n=\dfrac{360^{\circ}}{40^{\circ}}\)

\(\implies n=9\)

Therefore, the regular polygon has 9 sides.

To determine the length of each side, divide the given perimeter by the number of sides:

\(\implies \sf Side\;length=\dfrac{Perimeter}{\textsf{$n$}}\)

\(\implies \sf Side \;length=\dfrac{72}{9}\)

\(\implies \sf Side \;length=8\;ft\)

Therefore, the length of each side of the regular polygon is 8 ft.

\(\hrulefill\)

The area of a regular polygon can be calculated using the following formula:

\(\boxed{\begin{minipage}{5.5cm}\underline{Area of a regular polygon}\\\\$A=\dfrac{s^2n}{4 \tan\left(\dfrac{180^{\circ}}{n}\right)}$\\\\\\where:\\\phantom{ww}$\bullet$ $n$ is the number of sides.\\ \phantom{ww}$\bullet$ $s$ is the side length.\\\end{minipage}}\)

A regular pentagon has 5 sides, so n = 5.

If its perimeter is 50 inches, then the length of one side is 10 inches, so s = 10.

Substitute the values of s and n into the formula and solve for A:

\(\implies A=\dfrac{(10)^2 \cdot 5}{4 \tan\left(\dfrac{180^{\circ}}{5}\right)}\)

\(\implies A=\dfrac{100 \cdot 5}{4 \tan\left(36^{\circ}\right)}\)

\(\implies A=\dfrac{500}{4 \tan\left(36^{\circ}\right)}\)

\(\implies A=\dfrac{125}{\tan\left(36^{\circ}\right)}\)

\(\implies A=172.047740...\)

Therefore, the area of a regular pentagon with perimeter 50 inches is 172.0 in² rounded to the nearest tenth.

Answer:

1.695.29 m^2

2.8 feet

3. 172.0477 in^2

Step-by-step explanation:

1. The area of a regular octagon can be found using the formula:

\(\boxed{\bold{Area = 2a^2(1 + \sqrt{2})}}\)

where a is the length of one side of the octagon.

In this case, a = 12 m, so the area is:

\(\bold{Area = 2(12 m)^2(1 + \sqrt{2}) = 288m^2(1 + \sqrt2)=695.29 m^2}\)

Therefore, the Area of a regular octagon is 695.29 m^2

2.

The formula for the exterior angle of a regular polygon is:

\(\boxed{\bold{Exterior \:angle = \frac{360^o}{n}}}\)

where n is the number of sides in the polygon.

In this case, the exterior angle is 40°, so we can set up the following equation:

\(\bold{40^o=\frac{ 360^0 }{n}}\)

\(n=\frac{360}{40}=9\)

Therefore, the polygon has n=9 sides.

Perimeter=72ft.

We have

\(\boxed{\bold{Perimeter = n*s}}\)

where n is the number of sides in the polygon and s is the length of one side.

Substituting Value.

72 feet = 9*s

\(\bold{s =\frac{ 72 \:feet }{ 9}}\)

s = 8 feet

Therefore, the length of each side of the polygon is 8 feet.

3.

Solution:

A regular pentagon has five sides of equal length. If the perimeter of the pentagon is 50 in, then each side has a length = \(\bold{\frac{perimeter}{n}=\frac{50}{5 }= 10 in.}\)

The area of a regular pentagon can be found using the following formula:

\(\boxed{\bold{Area = \frac{1}{4}\sqrt{5(5+2\sqrt{5})} *s^2}}\)

where s is the length of one side of the Pentagon.

In this case, s = 10 in, so the area is:

\(\bold{Area= \frac{1}{4}\sqrt{5(5+2\sqrt{5})} *10^2=172.0477 in^2}\)

Drawing: Attachment

Answer:

Step-by-step explanation:

13.3 + 6.7 = 20

\(\frac{13.3}{20} = \frac{x}{x + 10} \\\\ 20x = 13.3(x + 10) \\\ 20x = 13.3x + 133 \\\ 20x - 13.3x = 133 \\\ 6.7x = 133 \\\ x = \frac{133}{6.7} \\\\ x ≈ 19.85 \\\ x ≈ 20\)

I hope I've helped you.

The value of the given expression in the standard form is 1.368×10².

We are given a mathematical expression. The expression consists of two arithmetic operations. First of all, two numbers are multiplied by each other, and then their result is divided by the third number. Let the mathematical expression be denoted by the variable "E". The expression is given below.

E = (4.56×3.6)/0.12

First, we will multiply the numbers in the numerator.

E = 16.416/0.12

Now we will divide the numerator by the denominator.

E = 136.8

Hence, the value of the expression is 136.8. Now we need to convert the resulting number into standard form. The standard form is given below.

E = 1.368×10²

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Answer:

height = 5 cm

Step-by-step explanation:

a cube has congruent sides (s)

the volume (V) of a cube is calculated as

V = s³

given V = 125 , then

s³ = 125 ( take cube root of both sides )

\(\sqrt[3]{s^3}\) = \(\sqrt[3]{125}\) = \(\sqrt[3]{5^3}\)

s = 5

then height = 5 cm

Answer:

Step-by-step explanation:

cos A = \(\frac{\sqrt{8} }{3}\)

The domain of (s - t)(x) in interval notation is (-∞, -8) U (-8, 5) U (5, 8) U (8,

∞).

To find (s - t)(x), we subtract the function t(x) from s(x).

s(x) =\((x - 5)/(x^2 - 64)\)

t(x) = (x - 8)/(5 - x)

To subtract the functions, we need a common denominator. In this case, we can use (x^2 - 64) as the common denominator.

(s - t)(x) =\([(x - 5)/(x^2 - 64)] - [(x - 8)/(5 - x)]\)

To simplify the expression, we need to factor the denominators and simplify further:

\((x^2 - 64) = (x - 8)(x + 8)\)

(5 - x) = -(x - 5)

Substituting these into the expression, we get:

(s - t)(x) = [(x - 5)/(x - 8)(x + 8)] - [(x - 8)/-(x - 5)]

Next, we need to find a common denominator for the two fractions. The common denominator will be (x - 8)(x + 8)(x - 5).

(s - t)(x) = [(x - 5)(-(x - 5))/((x - 8)(x + 8)(x - 5))] - [(x - 8)(x + 8)/((x - 8)(x + 8)(x - 5))]

Simplifying further:

(s - t)(x) = \([-(x - 5)^2 - (x - 8)(x + 8)]/[(x - 8)(x + 8)(x - 5)]\)

The domain of the function (s - t)(x) is the set of values for which the denominator is non-zero, since division by zero is undefined.

The denominator (x - 8)(x + 8)(x - 5) will be non-zero as long as x is not equal to 8, -8, or 5.

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Answer:

24

Step-by-step explanation:

5(2) + 7(2) = 10+14 = 24

Answer:

5+(n-1)0.5

Step-by-step explanation:

Answer:

12% alkaline

Step-by-step explanation:

The amount of 1% acid solution she needs to mix is 25 ml while the percentage of 5% acid solution she needs to mix is 75 ml.

Given to us

A chemist has a bottle of a 1% acid solution and a bottle of a 5% acid solution.

She wants to mix the two solutions to get 100 ml of a 4% acid solution.

Assumption

Let the amount of 1% acid solution be x ml, and the amount of 5% acid solution be y ml.

As the chemist wants to mix the two solutions to make 100 ml of solutions, therefore,

amount of 1% acid solution + amount of 5% acid solution = 100ml

x + y = 100.....equation 1

Solving for y,

y = 100 - x

We know that the mixture is having a 4% concentration and is 100 ml in volume.

\((1\%)x+(5\%)y = (4\%)100\\0.01x+0.05y=0.04\times 100\\\)

Substitute the value of y,

\(0.01x+0.05(100-x)=0.04\times 100\\\\0.01x + (0.05\times 100)-(0.05\times x) = 4\\\\0.01x + 5 -0.05x =4\\\\0.01x-0.05x = 4-5\\\\0.04x = 1\\\\x=\dfrac{1}{0.04}\\\\x = 25\ ml\)

Substitute the value of x in equation y,

\(x+y = 100\\25 +y =100\\y = 100-25\\y=75\ ml\)

Hence, the amount of 1% acid solution she needs to mix is 25 ml while the percentage of 5% acid solution she needs to mix is 75 ml.

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Answer:

x-7y=84

x-7y-84=0

Step-by-step explanation:

y=mx+c

y=ax+b

ax+by=c or ax+by-c=0

m= 1/7

y=1/7x-12

x-7y=84

x-7y-84=0

The value οf P(x > 104) is 0.1587 οr apprοximately 15.87%.

Prοbability is the study οf the chances οf οccurrence οf a result, which are οbtained by the ratiο between favοrable cases and pοssible cases.

Tο find the prοbability οf P(x > 104) fοr a nοrmal distributiοn with mean οf 98 and standard deviatiοn οf 6, we need tο standardize the value οf 104 using the fοrmula:

z = (x - μ) / σ

where z is the standard scοre, x is the value we want tο find the prοbability fοr, μ is the mean οf the distributiοn and σ is the standard deviatiοn.

Plugging in the values, we get:

z = (104 - 98) / 6 = 1

Nοw we need tο find the area tο the right οf this value οn the standard nοrmal distributiοn table οr calculatοr.

Using a standard nοrmal distributiοn table οr calculatοr, we find that the area tο the right οf z = 1 is 0.1587.

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Answer:

C: EAF Is the correct answer

Answer:

y=-3x+-1 or y=-3x-1; y intercepts(0,-1); x intercepts(0,1/3)

Step-by-step explanation:

y=mx+b

-1=-3*0+b

-1=0+b

(subtract 0 from both sides)

-1=b

So your equation will be: y=-3x-1

The equation of the line with a slope of -3 and y-intercept of -1 is given as y = -3x - 1. And the graph is shown below.

A Linear system is a system in which the degree of the variable in the equation is one. It may contain one, two, or more than two variables.

Write an equation in slope-intercept form for the line with slope -3 and y-intercept -1.

We know that the equation of the line is given as  

\(\rm y = mx +c\)

Where m is the slope and c is the y-intercept. Then the equation will be

\(\rm y = -3x - 1\)

Then the graph of the line is given below.

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The procedure using in setting class limits for a frequency distribution are given as follows:

A frequency distribution can show either the relative frequency (percentage) or the absolute frequency (number of observations) observed for each interval of a data-set.

These intervals are called the limits of the frequency distribution. To obtain the limits, these following features are needed:

Then the class width is calculated as follows:

Class width = (Maximum - Minimum)/Number of intervals.

This operation may result in a non-integer value, meaning that the class width may be rounded.

Then the classes are built as follows:

The problem is incomplete, hence the entire procedure to set class limits was described.

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Answer:

True

Step-by-step explanation:

The total flowers: bloom + not bloom

total: (3p + 1) + (2pm - 8) = 3p + 2p +1 -8 = 5p - 7

so the total of flowers is equal to the total planted by Caesar 5p - 7

Answer:

yes

Step-by-step explanation:

y + 4 = 12

Subtract 4 on both sides,

y + 4 - 4 = 12 - 4

y = 8