What is the radius of each figure described? a. A sphere with a volume of 500*3. 14/3 cm^3 b. A cylinder with a height of 3 and a volume of 147*3. 14 c. A cone with a height of 12 and a volume of 16*3. 14

Answer:

Stem | Leaf

1| 9

2| 5 9

3| 0 3 3 8

4| 0 7 9

5| 4 5

6| 1 5

7| 2 7

8| 1

Step-by-step explanation:

Minimum: 19

Maximum: 81

Range: 62

Count: 17

Sum: 808

Mean: 47.53

Median: 47

Mode: 33

Standard Deviation: 18.9

Variance: 357.3

The expression that represent the length of the rope is 10 / cos 40° =  13.1 feet

A 12-foot pole is supporting a tent and has a rope attached to the top. The rope is pulled straight and the other end is attached to a peg two foot above the ground.

This situation forms a right angle triangle. Therefore, let's find the expression that shows the length of the rope using trigonometric ratios.

Hence,

cos 40 = adjacent / hypotenuse

adjacent side = 10 ft

Therefore,

cos 40° = 10 / x

where

cross multiply

x = 10 / cos 40°

x = 10 / 0.76604444311

x = 13.0548302872

x = 13.1 feet

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The surface with equation (y^2 + 1)e^z – (z^2 + 1)e^x + y^2z^2e^y = 0 can be parametrized as follows 1:

x = u

y = v

z = ln((v^2 + 1) / (u^2 + 1))

Parametrization of a surface is a mathematical technique used to describe a surface in terms of parameters. It involves expressing the coordinates of points on the surface as functions of two or more parameters. A common way to parametrize a surface is to use two parameters u and v to represent the coordinates of points on the surface. This is called a parametric representation or a parametric equation of the surface. Another way to parametrize a surface is to use a vector-valued function, which maps a point in a domain onto a point on the surface. Both of these techniques allow us to describe the surface in a way that is useful for mathematical analysis and visualization.

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Answer:

1/3+(-2/5) and 1/3+2/5

Step-by-step explanation:

Answer:

2(1/2)(4)(5.5) + 2(1/2)(5)(6) + 4(6) =

22 + 30 + 24 = 76 square centimeters

B is correct.

Answer:

7/4, 9/4, 11/4, 13/4

Step-by-step explanation:

+ In an arithmetic sequence, to find the pattern you must subtract a term from the term after it to find the common difference.

3/4 subtracted from 5/4 is 2/4

1/4 subtracted from 3/4 is 2/4

+ So the common difference is 2/4 (Aka 1/2, but you want to keep the same denominator)

+ Therefore, between each new term, you add 2/4

1/4, 3/4, 5/4, 7/4, 9/4, 11/4, 13/4... and so on

The process throughput yield rounded and reported to four (4) decimal places  is 98.9189%.

To find the process throughput yield, follow these steps:
1. Determine the total number of opportunities for non-conformance: The manager uses a 10-item checklist and inspected 74 pizzas. Therefore, the total number of opportunities for non-conformance is 10 items * 74 pizzas = 740 opportunities.

2. Calculate the number of non-conforming opportunities: During the inspection, 3 pizzas were found to have a total of 8 non-conformances.

3. Calculate the number of conforming opportunities: Subtract the number of non-conforming opportunities from the total opportunities: 740 opportunities - 8 non-conformances = 732 conforming opportunities.

4. Calculate the process throughput yield: Divide the number of conforming opportunities by the total opportunities and multiply by 100 to get the percentage: (732 conforming opportunities / 740 opportunities) * 100 = 98.9189%.

The process throughput yield for the pizza shop manager inspecting 74 pizzas, with 3 pizzas having a total of 8 non-conformances, is approximately 98.9189%. When rounded and reported to four (4) decimal places, the answer is 98.9189%.

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There are 4 aces and 4 nights in a standard 52-card deck. So, the total number of cards that can be considered as a successful outcome is 8. Therefore, the probability of being dealt an ace or an 8 is 8/52 or 2/13. To find the probability of being dealt an Ace or an 8, follow these steps:

1. Identify the total number of cards in the deck: There are 52 cards in a standard deck.

2. Determine the number of Aces and 8s in the deck: There are 4 Aces and 4 eights, totaling 8 cards (4 Aces + 4 eights).

3. Calculate the probability: Divide the number of desired outcomes (Aces and 8s) by the total number of cards in the deck.

Probability = (Number of Aces and 8s) / (Total number of cards)
Probability = 8 / 52

4. Simplify the fraction: 8/52 can be simplified to 2/13.

So, the probability of being dealt an Ace or an 8 from a standard 52-card deck is 2/13.

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Answer: Y = 45x + 140

Step-by-step explanation:

which equation represents the length of the completed tunnel based on the number of days since tbm was introduced? the answer is y = 45x + 140

For a decimal number 0.54, the converted fraction from this decimal number is written as [tex]\frac{ 54}{100} [/tex]. After simplification, the required fraction is equals to the [tex]\frac{ 27}{50} [/tex].

A fraction is defined as a part of whole. It is expressed as a quotient, where the numerator is divided by the denominator. To convert a decimal to a fraction, first we place the decimal number over its place value. For example, in 0.4, the 4 is in the tenths place, so we place 4over 10 to create the equivalent fraction, 4/10. We can simplify this fraction. To write the decimal fraction in fraction form of the digits to the right of the decimal period (numerator) and a power of 10 (denominator).

We have a decimal number, 0.54. We convert it in a simplified fraction form. As we see decimal is placed on hundredth place. So, the required fraction is 54 over 100 or we can write [tex]\frac{ 54}{100} [/tex]. Simplify this fraction, dividing the denominator and numentor by 2 then, [tex]\frac{27}{50} [/tex]. Hence, required value is [tex]\frac{27}{50} [/tex].

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Answer: 50

Step-by-step explanation:

Answer:

50?

Step-by-step explanation:

10-5 equals 5

5+7 equals 12

12-2 equals 10

10-9 equals 1

1+2 equals 3

3-5 equals -2

-2+12 equals 10

10-3 equals 7

7+7 equals 14

14-3 equals 11

11+9 equals 20

20-10 equals 10

10-6 equals 4

4+8 equals 12

12-2 equals 10

10+60 equals 70

70-20 equals 50

Answer:

5xy + 6y

Step-by-step explanation:

4x(2y) + 3y(2-x)

= 8xy + 6y - 3xy

= 5xy + 6y

So, the answer is 5xy + 6y

The simplified expression is:5xy + 6y

Expanding the expression gives:

4x(2y) + 3y(2 - x) = 8xy + 6y - 3xy

Combining like terms, we get:

8xy - 3xy + 6y = 5xy + 6y

Therefore, the simplified expression is:

5xy + 6y

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Check the picture below.

so if we just get the volume of the whole box, and the volume of the balls, if we subtract the volume of the balls from that of the whole box, what's leftover is the part we didn't subtract, namely the empty space.

[tex]\stackrel{ \textit{\LARGE volumes} }{\stackrel{ whole~box }{(3.5)(3.5)(12.1)}~~ - ~~\stackrel{\textit{three balls} }{3\cdot \cfrac{4\pi (1.65)^3}{3}}} \\\\\\ 148.225~~ - ~~17.9685\pi ~~ \approx ~~ \text{\LARGE 91.8}~cm^3[/tex]

Answer:

8384742

Step-by-step explanation:

Answer:

there is no cow there because they have been barn

The image of the point after it is rotated 180° about the z-axis is A' = (1, -2, -2)

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

Point A = (-1, 2, 2)

The rule of rotation is given as rotated 180° about the z-axis

Mathematically, this rule can be expressed as

(x, y, z) = (-x, -y, -z)

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

A' = (1, -2, -2)

Hence. the image of the point after the rotation is A' = (1, -2, -2)

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The firm's weighted average cost of capital is 15.074%

To calculate the weighted average cost of capital (WACC), we need to follow these steps:

1. Determine the weight of each component of the capital structure (debt, preferred stock, and common stock) by dividing the value of each component by the total capital.
2. Multiply the weight of each component by its respective cost.
3. Sum the weighted costs to obtain the WACC.

Here's the step-by-step calculation:

1. Calculate the weights:
Debt weight = $1,083 / $5,032 = 0.215
Preferred stock weight = $268 / $5,032 = 0.053
Common stock weight = $3,681 / $5,032 = 0.732

2. Calculate the weighted costs:
Weighted cost of debt = 0.215 x 5.5% = 0.011825
Weighted cost of preferred stock = 0.053 x 13.5% = 0.007155
Weighted cost of common stock = 0.732 x 18% = 0.13176

3. Sum the weighted costs to find the WACC:
WACC = 0.011825 + 0.007155 + 0.13176 = 0.15074 or 15.074%

Therefore, we can state that the firm's weighted average cost of capital is 15.074%.

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Using the Alternate angles theorem, the value of x in the given diagram is 11

From the question, we are to calculate the value of x that will make A || B

From the Alternate angles theorem which states that when two parallel lines are cut by a transversal, then the resulting alternate interior angles or alternate exterior angles are congruent.

In the given diagram,

The angle measures (4x + 41) and (6x + 19) are alternate interior angle measures

Thus.

For A to be parallel to B (A || B)

4x + 41 = 6x + 19

Solve for x

4x + 41 = 6x + 19

41 - 19 = 6x - 4x

22 = 2x

Divide both sides by 2

22 / 2 = x

11 = x

x = 11

Hence,

The value of x is 11

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The PM of the circle is 6 in.

Since the diameter of the circle divide the circle into two equal parts. We can say:

PM = MQ

Applying the Intersecting Chord Theorem (When two chords intersect each other inside a circle, the products of their segments are equal). That is:

SM * RM = PM * MQ

SM * RM = PM²

SM = 13 - 4

SM = 9 in

RM = 4 in

Substituting:

SM * RM = PM²

9 * 4 = PM²

PM² = 36

PM = √36

PM = 6 in

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The greatest common factor of the given expression is 2.

The expression can be factored as (5x - 1)(x + 3).

Part A :

Given expression is 10x² + 28x - 6.

Greatest common factor of the expression is the greatest of all the common factors.

It is 2.

Therefore, the greatest common factor is 2.

Part B :

10x² + 28x - 6

5x² + 14x - 3

This can be factored as,

(5x - 1)(x + 3)

Part C :

(5x - 1)(x + 3) = (5x)(x) - (x) + (3)(5x) - 3

                    = 5x² + 14x - 3

Hence the GCF is 2.

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Answer:

Step-by-step explanation:To determine the line of reflection, we need to find the equation of the line that is equidistant from each vertex of the original triangle and the corresponding vertex of the reflected triangle.

First, let's find the coordinates of the image of each vertex under the reflection. Since F' is given as (2, 2), we can reflect F across the unknown line of reflection to find the image of D and E. The line of reflection must be equidistant from each of these pairs of corresponding points.

To reflect F across a vertical line, the x-coordinate of F' must be the same as that of F but with the opposite sign. The x-coordinate of F is -2, so the x-coordinate of its image F' must be 2. Similarly, the y-coordinate of F' is 2, which means that the line of reflection must pass through the point (2, 2).

To reflect D across the same line, we can draw a perpendicular bisector between D and its image D', which must intersect the line of reflection at a right angle. The midpoint of DD' lies on the line of reflection, and it is equidistant from D and D'. Using the midpoint formula, we find the midpoint of DD' to be ((-3+2)/2, (5+2)/2) = (-0.5, 3.5). Since this point lies on the line of reflection, we can use the point-slope form of a line to find the equation of the line passing through (2, 2) and (-0.5, 3.5):

(y - 2) = m(x - 2) (where m is the slope of the line of reflection)

Simplifying:

y - 2 = m(x - 2)

y = mx - 2m + 2

To find the value of m, we can use the fact that the midpoint of DE lies on the line of reflection as well. The midpoint of DE is ((-3-10)/2, (5+4)/2) = (-6.5, 4.5). Substituting these values into the equation of the line, we get:

4.5 = m(-6.5) - 2m + 2

2.5 = -8.5m

m = -0.294

Therefore, the equation of the line of reflection is:

y = -0.294x + 2.588

This line is not the x-axis, y-axis or the line y=x. Therefore, the line of reflection is neither the x-axis nor the y-axis, and it is not the line y = x.

Answer:

X-axis

Step-by-step explanation:

I am in the middle of taking the quiz and this is the answer I think would be correct!

The total surface area of the square pyramid is 585 in²

An equation is an expression that can be used to show the relationship between two or more numbers and variables using mathematical operators.

The area of a figure is the amount of space it occupies in its two dimensional state.

To get the surface area:

Area of base = 15 in * 15 in = 225 in²

Area of one triangle lateral face = (1/2) * 15 in * 12 in = 90 in²

Area of four triangle lateral face = 4 * 90 in² = 360 in²

Total surface area = 225 in² + 360 in² = 585 in²

The total surface area is 585 in²

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The volume of the whole lime represented by a sphere is given by  12 cubic centimeters.

Volume of the lime in hemispherical shape is equal to

= 6 cubic centimeters

Let us consider 'r' be the radius of the sphere.

Volume of hemisphere = ( 2/3 ) πr³

Volume of a sphere = ( 4 /3) πr³

Relation between volume of hemisphere and volume of a whole lime sphere

Volume of a whole lime sphere = 2 times of volume of hemisphere

⇒Volume of a whole lime sphere =  2 × 6

⇒Volume of a whole lime sphere =  12 cubic centimeters.

Therefore, the volume of the whole lime is equal to  12 cubic centimeters.

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The value of x is 88.22 units.

Given is right triangle, we need to find the value of x,

tan 60° = 85 / a

a = 85 / √3

a = 49

Now,

tan 30° = 85 / a + x

a+x = 85 ÷ 1/√3

a+x = 147.22

x = 147.2-49

x = 88.22

Hence, the value of x is 88.22 units.

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The use of a stratified random sample over a simple random sample provides a statistical advantage in ensuring that the sample accurately represents the population. Stratified random sampling involves dividing the population into subgroups or strata based on certain characteristics, such as age or income.

This allows for a more representative sample as it ensures that each stratum is represented proportionally in the sample. In contrast, a simple random sample does not take into account any characteristics or strata of the population, which may result in an unrepresentative sample. Therefore, the use of a stratified random sample provides a statistical advantage by reducing the potential for sampling bias and increasing the accuracy of the study's results.
In the context of your study, a statistical advantage of using a stratified random sample over a simple random sample is that it ensures greater representation and accuracy in the results.

In a stratified random sample, the population is first divided into distinct subgroups or strata based on specific characteristics, such as age, gender, or income. Then, a simple random sample is taken from each stratum. This method helps to better represent each subgroup in the sample, which in turn improves the overall accuracy of the results.

On the other hand, a simple random sample involves selecting individuals from the entire population without considering any specific characteristics. This approach may not adequately represent certain subgroups, leading to potential biases and less accurate results. In summary, stratified random sampling provides a statistical advantage over simple random sampling by ensuring a better representation of subgroups, leading to more accurate and reliable results.

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Answer:

(3,1)

Step-by-step explanation:

Answer:

The method of substitution involves three steps:

Solve one equation for one of the variables.

Substitute (plug-in) this expression into the other equation and solve.

Resubstitute the value into the original equation to find the corresponding variable.

Step-by-step explanation:

So the perfect square factors of 792 are 4, 9, 36, 144, 484, and 1089.

The prime factorization of 792 by dividing it by its smallest prime factor repeatedly:

792 ÷ 2 = 396

396 ÷ 2 = 198

198 ÷ 2 = 99

99 ÷ 3 = 33

33 ÷ 3 = 11

So the prime factorization of 792 is [tex]2^3 * 3^2 * 11.[/tex]

To find the perfect square factors, we can look for pairs of factors where both factors have even exponents.

The factors of 792 are: 1, 2, 3, 4, 6, 8, 11, 12, 18, 22, 24, 33, 36, 44, 66, 72, 88, 132, 198, 264, 396, and 792.

The perfect square factors of 792 are:

[tex]2^2 = 4\\2^2 * 3^2 = 36\\2^2 * 11^2 = 484\\3^2 = 93^2 * 4^2 = 144\\3^2 * 11^2 = 1089[/tex]

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The expected value E(X) is 5.6.

To find the expected value E(X) of the given data, we'll use the terms you provided: data points (5, 6, 8, 9), probabilities (0.2, 0.2, 0.2, 0.2), and the formula E(X) = Σ [x * P(X = x)].

Step 1: List the data points and their corresponding probabilities:
X: 5, 6, 8, 9
P(X = x): 0.2, 0.2, 0.2, 0.2

Step 2: Use the formula E(X) = Σ [x * P(X = x)] and plug in the values:
E(X) = (5 * 0.2) + (6 * 0.2) + (8 * 0.2) + (9 * 0.2)

Step 3: Calculate each term:
E(X) = 1 + 1.2 + 1.6 + 1.8

Step 4: Sum up the terms:
E(X) = 5.6

Step 5: Round your answer to one decimal place:
E(X) = 5.6

So, the expected value E(X) of the given data is 5.6.

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