The following cylinder has a volume of 20π cm3 and a height of 5 cm

What is the diameter of the cylinder? Remember, the diameter of a circle is two times its radius

The calculated productivities are:

Labor Productivity: 10 units per labor hour.

Multifactor Productivity: 0.8 units per dollar.

Energy Productivity: 20 units per dollar.

To calculate the labor productivity, divide the units produced by the labor hours:

Labor Productivity = Units Produced / Labor Hours

Labor Productivity = 10,000 / 1,000 = 10 units per labor hour.

To calculate the multifactor productivity, divide the units produced by the sum of labor, material, and energy costs:

Multifactor Productivity = Units Produced / (Labor Cost + Material Cost + Energy Cost)

In this case, the labor cost is $10 per labor hour, so the labor cost is 1,000 labor hours * $10 = $10,000.

The material cost is $2,000, and the energy cost is $500.

Multifactor Productivity = 10,000 / ($10,000 + $2,000 + $500)

Multifactor Productivity = 10,000 / $12,500 = 0.8 units per dollar.

Finally, to calculate the energy productivity, divide the units produced by the energy cost:

Energy Productivity = Units Produced / Energy Cost

In this case, the units produced are 10,000, and the energy cost is $500.

Energy Productivity = 10,000 / $500 = 20 units per dollar.

Therefore, the calculated productivities are:

Labor Productivity: 10 units per labor hour.

Multifactor Productivity: 0.8 units per dollar.

Energy Productivity: 20 units per dollar.

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Answer:

15 °C

Step-by-step explanation:

°C = (°F - 32) * (5/9)

Given that the initial temperature was 77 °F and it dropped by 10 °C, we can calculate the final temperature.

Initial temperature: 77 °F

Converting to Celsius:

°C = (77 - 32) * (5/9)

°C ≈ 25

The temperature dropped by 10 °C, so the final temperature is:

Final temperature = Initial temperature - Temperature drop

Final temperature ≈ 25 - 10 = 15 °C

Therefore, the temperature after the storm was approximately 15 °C.

All the slopes of tables are,

13) m = 2

14) m = - 1/1

15) m = 0

16) m = 3

17) m = infinite

18) m = - 1/3

We have to given that;

All the tables are shown.

And, To find the slope of all the table.

Since, We know that;

Slope passing through the points (x₁ , y₁) and (x₂, y₂) is defined as,

⇒ m = (y₂ - y₁) / (x₂ - x₁)

Hence, We get;

13) Two points are (- 2, - 3) and (- 1, - 1)

Hence, Slope is,

m = (- 1 + 3) / (- 1 + 2)

m = 2/1

m = 2

14) Two points are (- 4, 6) and (0, 4)

Hence, Slope is,

m = (4 - 6) / (0 + 4)

m = - 2/4

m = - 1/2

15) Two points are (6, 2) and (3, 2)

Hence, Slope is,

m = (2 - 2) / (3 - 6)

m = 0

16) Two points are (- 2, - 3) and (0, 3)

Hence, Slope is,

m = (3 + 3) / (0 + 2)

m = 6/2

m = 3

17) Two points are (3, 6) and (3, 4)

Hence, Slope is,

m = (4 - 6) / (3 - 3)

m = infinite

18) Two points are (- 4, 4) and (- 1, 3)

Hence, Slope is,

m = (3 - 4) / (- 1 + 4)

m = - 1/3

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The fraction of the cans in George’s pantry which are either soup or vegetables is 11/24.

Fraction of cans in George‘s pantry that are vegetables = 1/8

Fraction of cans in George‘s pantry that are soups = 1/3

Fraction of the cans in George’s pantry which are either soup or vegetables = 1/3 + 1/8

= (8+3) /24

= 11/24

Hence, 11/24 is the fraction of the cans in George’s pantry that are either soup or vegetables.

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The correct interpretation of the slope and y-intercept of the equation y = mx + b in this context is:

A. The slope predicts a temperature increase of about 50° for every increase of 1 chirp per minute. The y-intercept shows that when the crickets are not chirping (x=0), the temperature is 0.

In other words, according to the given equation, for each additional chirp per minute, the temperature is expected to increase by approximately 50 degrees Fahrenheit. Additionally, when there are no chirps (x=0), the equation suggests that the temperature is 0 degrees Fahrenheit.

~~~Harsha~~~

Answer:

C

Step-by-step explanation:

I am pretty certain the math is incorrect on the other posted answer

The slope is   rise/run   means every degree produces 6 chirps more ....or conversely , 1/6 degree produces one more chirp.  

  when the temperature is 50 F there are ZERO chirps

Answer:

  (d)  (0, 0), (0, 9), (9, 0)

Step-by-step explanation:

You want to know the vertices represented by the matrix 3T, where ...

  [tex]T=\left[\begin{array}{ccc}0&0&3\\0&3&0\end{array}\right][/tex]

The scaled matrix 3T is found by multiplying each element by the scale factor:

  [tex]3T=\left[\begin{array}{ccc}0&0&9\\0&9&0\end{array}\right][/tex]

Each column is an (x, y) pair representing a vertex. The vertices of the scaled triangle are ...

  (0, 0), (0, 9), (9, 0)

<95141404393>

The required selling price of each water bottle is $554.06 such that Michelle's robotics club will achieve 25% increase in the purchase price.

Given that number of water bottles purchased is 75 and cost price (C,P) of the 75 water bottles is $443.25. The increase %  on the purchase price is profit % = 25%.

To calculate the selling price when cost price and profit % is given by following steps:

Step 1 - Calculate the 25% of the cost price which gives profit.

Step 2 - Calculate SP, Selling price = Cost price + profit.

That implies, Profit = 25% of C.P.

Profit = 25/100 × 443.25.

Therefore, Profit = $110.81.

That implies, Selling price(S.P) = Cost price + profit.

S.P = 443.25 + 110.81.

Thus, S.P = $554.06.

Hence, the required selling price of each water bottle is $554.06 such that Michelle's robotics club will achieve 25% increase in the purchase price.

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Answer:

670

We can use the pythagorus theorum which says

The square of hypotenuse is equal to the square of perpendicular added to sq of base

Step-by-step explanation:

Use h2=p2+b2

H=6.708

Rounding to the hundredth place the answer is 670.8

Using Pythagoras Theorem (since the triangle is a right angled triangle)

[tex]( {hyp}^{2}) = ( {base}^{2} ) + ( {per}^{2} )[/tex]

[tex]( {hyp}^{2} ) = ( {3}^{2} ) + ( {6}^{2}) [/tex]

[tex]( {hyp}^{2} ) = 9 + 36[/tex]

[tex] {hyp}^{2} = 45[/tex]

Taking under root on both sides

[tex]hyp = 6.7[/tex]

Hence the missing side is 671

The translated coordinates are:

A: A'(-6, -5)  ⇒ A''(-3,-7)

B:  D'(2,-5)  ⇒  D''(8, -7)

C: C (2, 0)   ⇒ C'(5, -2)

D: D(5,-5)    ⇒ D'(8, -7)

E; C'(-1,0)     ⇒ C''(2, -2)

F: A (-3,-5)   ⇒ A'(0, -7)

G: B'(-5, 0 ) ⇒  B''(-2, -2)

H: B (-2, 0)  ⇒  B'(1, -2)

Here,

We have to apply a translation of 2 units down and 3 units right to these coordinates.

Translation means moving the entire polygon in a particular direction by a certain distance.

To apply the translation,

Add the same amount of distance to the x-coordinate of each vertex for the rightward motion, and subtract the same amount of distance from the y-coordinate of each vertex for the downward motion.

In this case,

the translation is 2 units down and 3 units right.

So the new coordinates will be:

A: A'(-6, -5) ⇒ A'( -6+ 3, -5-2)

              = A''(-3,-7)

B:  D'(2,-5)  ⇒ D'(5+3, -5 -2 )

                  = D''(8, -7)

Similarly apply for each coordinates we get,

C: C (2, 0)   ⇒ C'(5, -2)

D: D(5,-5)    ⇒ D'(8, -7)

E; C'(-1,0)     ⇒ C''(2, -2)

F: A (-3,-5)   ⇒ A'(0, -7)

G: B'(-5, 0 ) ⇒  B''(-2, -2)

H: B (-2, 0)  ⇒  B'(1, -2)

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The quantities in the two columns cannot be compared due to the absence of specific point values. D.

The given question presents two columns, Column A and Column B, representing the slopes of lines through different sets of points.

The actual points themselves are not provided in the question.

Without the specific point values, it is not possible to determine the slope values or compare the quantities in Column A and Column B.

The slope of a line is determined by the change in the y-coordinate divided by the change in the x-coordinate between two points.

Since the coordinates of the points are missing, it is impossible to calculate the slopes accurately or make any comparison between the quantities in Column A and Column B.

Without the points, it is not possible to determine the slopes or establish any relationship between the quantities in Column A and Column B.

To draw any conclusions or comparisons, the coordinates of the points through which the lines pass are crucial.

Without that information, we lack the necessary data to assess the slopes and make any meaningful comparison.

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The complete statements are;

m<Y = 90 degrees

m<M = 56.3 degrees

m<Z = 57 degrees

XY = 8

YZ = 12

To determine the values, we need to know the following;

From the image shown, we have that;

1. The measure of <Y is 90 degrees; angle at right angle

2. For m<M , we have;

Using the tangent identity, we have;

tan M = 12/8

tan M = 1.5

M = 56. 3 degrees

3. For m<Z, we have;

33 + m<Y + m<Z = 180

collect like terms

m<Z = 57 degrees

4. NM = XY

XY = 8

5, YZ = 12

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The statement, yes, they are independent because P(student) = 0.8 and P(student | logo A) = 0.8.

To determine if being a student and preferring logo A are independent events, we need to compare the probabilities of these events occurring.

The probability of being a student, denoted as P(student), is given as 0.8. This means that out of the total population (125), 80% are students.

The probability of a student preferring logo A, denoted as P(student | logo A), is given as 0.8.

This means that out of the students (100), 80% prefer logo A.

If the events of being a student and preferring logo A are independent, then the probability of a student preferring logo A (P(student | logo A)) should be the same as the probability of being a student (P(student)).

However, in the given options, both options A and D state that P(student | logo A) = 0.8, which is the same as P(student).

This suggests that being a student and preferring logo A are independent events.

Hence, Yes, they are independent because P(student) = 0.8 and P(student | logo A) = 0.8.

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The minimum selling price on the special order to produce net income of 5.17 per basketball is $ 29.79 per ball.

Variable cost of goods sold for the special order = $ ( 3,582,000 - 960,000 ) / 120,000 * 10,000 = $ 218,500

Variable selling and administrative expenses for special order = $ [( 513,400 - 271,000) / 120,000 + 0.75] x 10,000 = $ 27,700

Fixed costs are not relevant, as they would remain unchanged.

c. Profit required = $ 5.17 x 10,000 = $ 51,700

Minimum selling price required = $ ( 51,700 + 218,500 + 27,700) / 10,000

= $ 29.79 per ball.

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ThreePoint Sports Inc. manufactures basketballs for the Women's National Basketball Association (WNBA). For the first 6 months of 2017, the company reported the following operating results while operating at 80% of plant capacity and producing 120,000 units.What is the minimum selling price on the special order to produce net income of 5.17 per basketball

The statement that, the value 3π/4 is a solution for the equation 3√2 sec θ + 7 = 1 is true.

Given an equation,

3√2 sec θ + 7 = 1

We have to find that whether 3π/4 is a solution for the given equation or not.

Solving the given equation, we get,

3√2 sec θ + 7 = 1

3√2 sec θ = 1 - 7

3√2 sec θ = -6

sec θ = -6 / 3√2

sec θ = -2 / √2

sec θ = -√2

Now, we know that, sec θ = 1/ cos θ

So the equation becomes,

1/ cos θ = -√2

cos θ = -1/√2

Thus the solutions for the given equation are all values of θ such that cos θ = -1/√2.

cos 3π/4 =  cos (π - π/4) = -cos (π/4) = -1/√2

So 3π/4 is a solution for the equation 3√2 sec θ + 7 = 1.

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We are given two curves on a graph paper and we have to find the y values for the given x.

From the graph we can check for a value of x, what is the value of y from the curve.

x     -3     -2     -1    0      1         2        3

Exp  8      4      2    1      0.5  0.25  0.125

Lin.   7.5   6    4.5   3      1.5     0     -1.5

We find that the two have the same values where the two curves intersect.

From the graph we find that near to -3 and near to 2 both have the same values.

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The missing graph is attached below.

[tex]X'=\varepsilon\setminus X[/tex] where [tex]\varepsilon[/tex] is the universe. It means that [tex]X'[/tex] is everything except the set [tex]X[/tex], and that in shown in the image C.

Answer:

  {3, 4, 5}

Step-by-step explanation:

You want the integer values that satisfy the inequality 3 ≤ x < 6.

The interval of interest has an open circle at 6, which means x=6 is not included in the solution set. (The "or equal to" condition is missing there.) The integers that are included are shown in the attachment.

  {3, 4, 5} . . . . possible integer values of x

<95141404393>

Answer:

Algebra is the study of variables and the rules for manipulating these variables in formulas; it is a unifying thread of almost all of mathematics. Elementary algebra deals with the manipulation of variables as if they were numbers and is therefore essential in all applications of mathematics.

The commutative rule of addition, the commutative rule of multiplication, the associative rule of addition, the associative rule of multiplication, and the distributive property of multiplication make up the fundamental rules of the algebra.

ps. i copy from the internet

The length and width of the wall of the barn are 2 feet and 12 feet

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

The area of a rectangle is calculated as

Area  = Length * Width

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

x * (2x + 8) = 24

Express 24 as 2 * 12

So, we have

x * (2x + 8) = 2 * 12

This means that

x = 2 and 2x + 8 = 12

Evaluate

x = 2

Hence, the length of the rectangle is 2 feet

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Answer:

Step-by-step explanation:

To solve for m/MNP if m/MNO = 132° and m/PNO = 40°, we can use the fact that the sum of the angles in a triangle is 180 degrees.

First, we can find the measure of angle MNO:

m/MNO + m/PNO + m/MNP = 180

132 + 40 + m/MNP = 180

m/MNP = 8

Copy

Therefore, m/MNP = 8 degrees.

I hope this helps! Let me know if you have any other questions.

Answer:

Hope this saved you ^^

Step-by-step explanation:

To determine the number of babies we can expect among the next 12 children to enroll, we need to calculate the proportion of babies based on the current enrollment data.

Out of the total enrollment so far, there are 3 babies and 6 children of other ages, making a total of 9 children.

Proportion of babies = (Number of babies / Total number of children) = 3 / 9 = 1/3

Now, to estimate the number of babies among the next 12 children, we multiply the proportion of babies by the total number of children to be enrolled:

Number of babies expected = Proportion of babies * Total number of children to enroll

Number of babies expected = (1/3) * 12 = 4

Therefore, based on the current enrollment data, we can expect approximately 4 out of the next 12 children to be babies.

Answer:

  2.5%

Step-by-step explanation:

You want the percentage below 335 if the distribution is normal with a mean of 555 and a standard deviation of 110, using the empirical rule.

The z-score of 335 is ...

  Z = (X -µ)/σ

  Z = (335 -555)/110 = -220/110 = -2

The empirical rule tells you that 95% of the distribution is between Z = -2 and Z = 2. That is, 5% of the distribution is evenly split between the tails Z < -2 and Z > 2. Half that value is in each tail.

  P(X < 335) = 5%/2 = 2.5%

The percentage of people taking the test who score below 335 is 2.5%.

<95141404393>

Answer:

[tex]u+v=4.1\langle\cos160^\circ,\sin160^\circ\rangle[/tex]

Step-by-step explanation:

When adding two vectors, we add their horizontal components, and then their vertical components:

[tex]u=2\langle\cos325^\circ,\sin325^\circ\rangle=\langle2\cos325^\circ,2\sin325^\circ\rangle\\v=6\langle\cos155^\circ,\sin155^\circ\rangle=\langle6\cos155^\circ,6\sin155^\circ\rangle\\\\u+v=\langle2\cos325^\circ+6\cos155^\circ,2\sin325^\circ+6\sin155^\circ\rangle\\u+v\approx\langle-3.8,1.39\rangle[/tex]

We are not done however as we need to now calculate the magnitude and the direction of the resultant vector:

Magnitude:

[tex]||u+v||=\sqrt{(-3.8)^2+1.39^2}\approx4.1[/tex]

Direction:

[tex]\displaystyle \theta=tan^{-1}\biggr(\frac{1.39}{-3.8}\biggr)\approx-20^\circ=180-20^\circ=160^\circ[/tex]

Therefore, the resultant vector is about [tex]4.1\langle\cos160^\circ,\sin160^\circ\rangle[/tex]

Answer:

-----------------

The y-intercept of (0, 4) means the function has a value of 4 when x = 0.

Verify it with given functions:

A) y = 3x + 1

B) y = 4ˣ

C) y = 1ˣ

D) y = 2ˣ + 3

Answer:

BOYS = 30.

GIRLS = 12.

Step-by-step explanation:

Boys: B

Girls: G

B = (2/5)G

B + G = 42.

(2/5)G + G = 42

2G + 5G = 210

7G = 210

G = 210/7

G = 30.

B = (2/5)G

B = (2/5)(30)

B = 60/5

B = 12.

Answer:

[tex]\Huge \boxed{\bold{\text{12 Boys}}}[/tex]

[tex]\Huge \boxed{\bold{\text{30 Girls}}}[/tex]

Step-by-step explanation:

Let the number of girls be [tex]g[/tex] and the number of boys be [tex]b[/tex].

According to the problem: [tex]b = \frac{2}{5} \times g[/tex]

We also know that the total number of students is 42, so [tex]b + g = 42[/tex].

Now, we have two equations with two variables:

We can solve these equations to find the values of [tex]b[/tex] and [tex]g[/tex].

Step 1: Solve for [tex]\bold{b}[/tex] in terms of [tex]\bold{g}[/tex]

From the first equation, we have[tex]b = \frac{2}{5} \times g[/tex]

Step 2: Substitute the expression for [tex]\bold{b}[/tex] into the second equation

Replace [tex]b[/tex] in the second equation with the expression we found in step 1.

[tex]\frac{2}{5} \times g + g = 42[/tex]

Step 3: Solve for [tex]\bold{g}[/tex]

Now, we have an equation with only one variable, [tex]g[/tex]:

[tex]\frac{2}{5} \times g + g = 42[/tex]

To solve for [tex]g[/tex], first find a common denominator for the fractions:

[tex]\frac{2}{5} \times g + \frac{5}{5} \times g = 42[/tex]

Combine the fractions:

[tex]\frac{7}{5} \times g = 42[/tex]

Now, multiply both sides of the equation by [tex]\frac{5}{7}[/tex] to isolate [tex]g[/tex]:

Step 4: Find the value of [tex]\bold{b}[/tex]

Now that we have the value of [tex]g[/tex], we can find the value of [tex]b[/tex] using the first equation:

So, there are 12 boys and 30 girls in the class.

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Answer:

16 liters of the 10% acid solution should be in the mixture.

Step-by-step explanation:

Let x represent the volume of the 10% acid solution to be added.

The volume of pure acid added would be (90 - x).

The equation to solve is: 0.1x + (90 - x) = 0.84(90)

Simplifying, we get: 0.1x + 90 - x = 75.6

Combining like terms, we have: -0.9x + 90 = 75.6

Subtracting 90 from both sides: -0.9x = -14.4

Dividing by -0.9: x = 16

Therefore, 16 liters of the 10% acid solution should be in the mixture.

Based on fractional subtraction, Emily must walk ¹/₂₀ miles after dinner to meet her target walking distance of ⁴/₅ miles daily.

A fraction represents a portion or part of a whole value.

Subtractions involving fractions can be accomplished by finding the common factor of the denominators as follows:

The target walking distance that Emily set = ⁴/₅ miles

The distance Emily covered to work = ²/₅ miles

The distance Emily covered during lunchtime = ¹/₄ miles

The distance that Emily needs to walk after dinner to meet her set target = ¹/₂₀ (⁴/₅ - ²/₅ - ¹/₄)

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To stay healthy, Emily decided to walk 4/5 miles every day. She walked 2/5 miles to work and walked 1/4 mile at lunchtime. How much more does she need to walk after dinner if she wants to meet her target distance? ​