What is the volume of this object
cubic units

Answer:

3

Step-by-step explanation:

(volume)  21 * pi = 65.9734457254

height =7

Cone = (1/3)πr²h, where r is the radius and h is the height.

V = Ah/3

Answer:

2 2/3

Step-by-step explanation:

To minimize costs, the optimal distribution schedule for Finnish Furniture would involve shipping 130 units from Reno to Phoenix, 20 units from Denver to Cleveland, and 160 units from Pittsburgh to Chicago. This allocation is determined by using the transportation algorithm, specifically the Vogel's Approximation Method (VAM), which considers the lowest shipping costs per unit for each source-destination combination. By following this approach, the total cost for the distribution is calculated to be $4,360.

To determine the optimal distribution schedule that minimizes costs, we need to allocate the available supplies from the manufacturing facilities to the retail stores based on the shipping costs per unit. We can achieve this by employing the transportation algorithm, such as the North-West Corner Rule or the Vogel's Approximation Method (VAM).

Using VAM, we begin by identifying the lowest shipping cost per unit for each row and column in the given table. We then select the highest difference between the two lowest costs, considering both rows and columns. This difference indicates the most cost-effective allocation.

In this case, the VAM suggests shipping 130 units from Reno to Phoenix since the shipping cost per unit is 10, which is the lowest for the Reno row. For Cleveland, Denver has the lowest cost at 14, so we allocate 20 units from Denver to Cleveland. Lastly, we allocate 160 units from Pittsburgh to Chicago, as the cost per unit is the lowest at 12 for the Pittsburgh column.

Now, let's calculate the total cost. The cost of shipping 130 units from Reno to Phoenix is 130 x 10 = $1,300. Shipping 20 units from Denver to Cleveland costs 20 x 14 = $280. Lastly, shipping 160 units from Pittsburgh to Chicago costs 160 x 12 = $1,920. Adding these costs together gives us a total cost of $1,300 + $280 + $1,920 = $4,360.

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Answer:

12:30 PM

Step-by-step explanation:

In 2 hours (8:30 AM and 10:30 AM) she filled half of the full pond.

So to fill the other half we double how long it has taken her to do the first half assuming she doesn't stop. Therefore, the answer will be 12:30 PM

MAKE SURE TO WRITE PM AS IT IS AT MIDDAY

Answer:

Hello, the pool will be full at 12:30 PM. 1200 gallons is half of the capacity of the pool (2400), and the pool was half full at 10:30 AM after being run since 8:30 AM - two hours. This means that the pool will only need two more hours to fill up, and it will be full at 12:30 in the afternoon.

Have a great day! - Mani :)

Answer:

1

2,3,4

Step-by-step explanation: to

when the number of football is 1 is less expensive than basketball

The combined total number of miles Charlie biked in the two days can be expressed as the product of the average speeds for each day multiplied by the corresponding time durations.

Let's denote the number of hours Charlie biked yesterday as "x". According to the given information, his average speed on that day was "y" miles per hour. Therefore, Charlie traveled a distance of "xy" miles during yesterday's ride.

On the second day, Charlie biked for a total of (24 - x) hours, as the combined duration of the two days is given as 24 hours. His average speed on the second day was "z" miles per hour, resulting in a distance of (24 - x)z miles traveled.

To find the combined total number of miles Charlie biked in the two days, we need to sum up the distances traveled on each day. Therefore, the expression for the combined total number of miles is xy + (24 - x)z.

In summary, the expression for the combined total number of miles Charlie biked in the two days is xy + (24 - x)z, where "x" represents the number of hours he biked yesterday, "y" represents his average speed on that day, and "z" represents his average speed on the second day.

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Answer:

Option C

x²+ 2x -24=0

x²+6x-4x-24= 0

x(x+6) -4(x+6) = 0

(x+6)(x-4) = 0

x= -6 and 4

Therefore, for x = 4 and -6 , the above given equation is true.

The characteristics of the coefficient of variation are:

(a) It adjusts for differences in the

magnitude of means.

(c) It allows for direct comparisons across different

data sets.

The coefficient of variation (CV) is a statistical measure that expresses the relative variability of a dataset. It is calculated by dividing the standard deviation of the data by the mean and then multiplying by 100 to express it as a percentage.

(a) The coefficient of variation adjusts for differences in the magnitude of means. This means that it takes into account the scale or magnitude of the mean value when measuring the variability. By dividing the standard deviation by the mean, the

CV

provides a normalized measure of variability that can be used to compare datasets with different mean values.

(c) The coefficient of variation allows for direct comparisons across different data sets. Since the CV is expressed as a percentage, it provides a standardized measure of variability that can be used to compare datasets regardless of the

units of measurement

. This makes it particularly useful when comparing variability in datasets with different scales or units.

(d) It is important to note that the coefficient of variation is not a measure of central location. It is a measure of

relative variability

and does not provide information about the central tendency or location of the data.

Therefore, the characteristics of the coefficient of variation are that it adjusts for differences in the

magnitude

of means and allows for direct comparisons across different data sets. It is not a measure of central location and does not have the same units of measurement as the observations.

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In this figure ∠7 and ∠3 are alternate interior angles . Alternate interior angles in two parallel lines with a transversal will always be equal . Since ∠7 is congruent to ∠3 , we can say that line m and line n are parallel lines .

Therefore :-

The lines are parallel because the alternate interior angles in them are congruent .

Given :-

m∠3 = ( 15x + 22 )°

Then , m∠3 will be equal to :-

x = 8

= 15 × 8 + 22

= 120 + 22

m∠3 = 142°

m∠1 = ( 19x - 10 )°

= 19 × 8 - 10

= 152 - 10

m∠1 = 142°

angle 1 and angle 3 are corresponding angles , which means their value will be equal if they are present on two parallel lines with a transversal . As their values are equal we can say that line m and line n are parallel .

Therefore :-

Yes , the lines are parallel because the corresponding angles in them are equal .

∠7 and ∠6 are interior angles on the same side of transversal , which means their angle su, will be equal to 180° . But since their values are equal these two lines are not parallel .

Therefore :-

∠7 and ∠6 are interior angles on the same side of transversal , so their sum will be equal to 180° . But since that is not the case in the lines shown above , those lines are not parallel lines .

Given :-

m∠2 = ( 5x + 3 )°

x = 14

= 5 × 14 + 3

= 60 + 3

= 63°

m∠3 = ( 8x - 5 )°

= 8 × 14 - 5

= 112 - 5

= 107°

We know that the sum of angle 2 and angle 3 will be equal to 180° if they are on two parallel lines as they are interior angles on the same side of transversal .

As :-

∠2 + ∠3 ≠ 180°

63° + 107° is not equal to 180° ,

Therefore :-

These lines are not parallel as the sum of their interior angles on the same side of transversal is not equal to 180°.

Given :-

m∠8 = ( 6x - 1 )°

x = 9

= 6 × 9 - 1

= 54 - 1

= 53°

m∠4 = ( 5x + 3 )°

= 5 × 9 + 3

= 45 + 3

= 48°

angle 8 and angle 2 are vertically opposite angles , which means m∠8 = m∠2 .

m∠2 = 53°

As ∠2 and ∠4 are corresponding angles their value will be equal , if they are on parallel lines .

Since angle 2 , angle 8 and angle 4 are not equal these lines are not parallel lines .

Therefore :-

The lines are not parallel as their corresponding angles are not equal .

Angle 5 and angle 7 are corresponding angles they will be congruent when on parallel lines .

As , m∠5 ≅ m∠7 these lines are parallel .

Therefore :-

These lines are parallel lines as their corresponding angles are equal .

Angle 1 and angle 7 are vertically opposite angles , which means their angle measure will be equal . As angle 7 and angle 5 are corresponding angles their angle measure will also be equal .

Since m∠5 ≅ m∠7 , these lines are parallel .

Therefore :-

These lines are parallel lines as their corresponding angles are equal .

Here , the value of x is the same .

Which means :-

m∠2 = x + 15° is greater than m∠6 = x + 10°

Angle 2 and angle 6 are alternate interior angles , their values should be equal . But since their values are not equal , the lines on which they reside are not parallel .

Therefore :-

These lines are not parallel as their alternate interior angles are not equal .

It is given that angle 1 and angle 3 are supplementary angles . It is also clear that angle 1 and angle 2 are a linear pair , which means their angle sum will be equal to 180° . Also , angle 3 and angle 2 should be equal since they are the supplement of the same angle . Angle 2 and angle 3 are also corresponding angles . Since corresponding angles in two lines with a transversal will be equal and in these two lines the corresponding angles are equal , these lines are parallel lines.

Therefore , JK // HI as their corresponding angles are equal .

Answer:

C

Step-by-step explanation:

So we have the function:

\(h(t)=120t-16t^2\)

Where h(t) measures the height after t seconds.

To find the height of the object after 6 seconds, substitute 6 for t. So:

\(h(t)=120(6)-16(6)^2\)

Evaluate. Square:

\(h(t)=120(6)-16(36)\)

Multiply:

\(h(6)=720-576\)

Subtract:

\(h(6)=144\)

So, the height after six seconds of the object is 144 ft.

Our answer is C.

The value of x from the relation is x= a/b √(y²a² - b²).

We have,

y=√x²b²- a²b² ÷ a²

Now, we have to find the value of x

y=√x²b²- a²b² ÷ a²

ya² = √x²b² - a²b²

ya² = √b²(x²- a²)

ya²= b √ x² - a²

ya²/b = √x²-a²

Now, taking square on both side we get

y²\(a^4\) / b² = x² - a²

x² = y²\(a^4\) / b² - a²

x² = (y²\(a^4\) - a²b²)/ b²

x= √(y²\(a^4\) - a²b²)/ b²

x= a/b √(y²a² - b²)

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The true statement regarding the facts provided in the table is given by: Option D:  the payment amount each month stays the same.

Amount whose value increases from its past value is called increasing amount.

The missing table is attached below.

Checking the validity of each option:

We see from the table that interest in each previous month is bigger than next month, for example, in first month, it was $56.33, and in next month, it was $54.99, so interest is decreasing.

Thus, this option is not correct.

The principal amount in any previous month is smaller than the next month principal amount. For example, in first month, the principal amount was $184.96 and in next month, it became $186.33, so the principal amount is increasing.

Thus,  this option is not correct.

Option C is false and option D is true. It is because the payment is constant $241.32(iie, it doesn't change, and therefore stays the same) in each of the months.

Thus, the true statement regarding the facts provided in the table is given by: Option D:  the payment amount each month stays the same.

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The inverse of the function y = x^2 + 1 is given by y = ±√(x - 1).

To find the inverse of the function y = x^2 + 1, we need to interchange the roles of x and y and solve for the new y.

Start with the equation y = x^2 + 1.

Step 1: Interchange x and y: x = y^2 + 1.

Step 2: Solve for y: y^2 = x - 1.

Step 3: Take the square root of both sides: y = ±√(x - 1).

The inverse of the function y = x^2 + 1 is given by y = ±√(x - 1).

However, note that the inverse is not a function because for each value of x, there are two possible values for y (positive and negative square roots). Therefore, the inverse is not a one-to-one mapping, which is a requirement for a function.

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Answer:

Lets take all factors into consideration first

The door is a rectangle and the area of a rectangle is length times width

Let the width be w

Let the length be l

Equation length × breadth = area

(w+48)w = 3024

w^2 + 48w = 3024

w^2 + 48w - 3024 = 0

w^2 + 84w - 36w - 3024 = 0

w(w + 84) -36 ( w + 84) = 0

(w + 84) (w - 36) = 0

w + 84 = 0 AND w - 36 =0

w = -84 and w = 36

Since width cannot be negative, the right answer is 36

How did I get 84 and 36? Well, I had to factorize 3024 and since 84 times 36 is 3024 and 84 minus 36 is 48, I chose them.

Answer:

1. I don't know how to solve that sorry :(

2. B. It is a diameter

3. 30° = q

4. I don't know sorry :(

Step-by-step explanation:

1. I don't know how to solve that sorry :(

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

2. B. It is a diameter

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

3. All triangles = 180°

180° = 60° + 90° + q

180° = 150° + q

180° - 150° = 150° - 150° + q

30° = q

180° = 60° + 90° + 30°

180° = 150° + 30°

180° = 180°

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

4. I don't know sorry :(

To determine if a system of linear equations has infinitely many solutions, you need to solve the system and check the resulting equations.

Here are the general steps:

If you obtain a valid solution for each variable, then the system has a unique solution.

If you have two or more variables and only obtain a solution for some of them, then the system has infinitely many solutions.

It's also important to note that if you have a system with fewer equations than variables, it may also have infinitely many solutions.

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Answer: the price of one senior citizen ticket is $10, and the price of one student ticket is $5.

Step-by-step explanation:

Let's assume the price of one senior citizen ticket is 's' dollars and the price of one student ticket is 't' dollars.

According to the given information, on the first day, the school sold 7 senior citizen tickets and 11 student tickets, totaling $125. This can be expressed as the equation:

7s + 11t = 125 ---(1)

On the second day, the school sold 14 senior citizen tickets and 8 student tickets, totaling $180. This can be expressed as the equation:

14s + 8t = 180 ---(2)

We now have a system of two equations with two variables. We can solve this system to find the values of 's' and 't'.

Multiplying equation (1) by 8 and equation (2) by 11, we get:

56s + 88t = 1000 ---(3)

154s + 88t = 1980 ---(4)

Subtracting equation (3) from equation (4) eliminates 't':

(154s + 88t) - (56s + 88t) = 1980 - 1000

98s = 980

s = 980 / 98

s = 10

Substituting the value of 's' back into equation (1), we can solve for 't':

7s + 11t = 125

7(10) + 11t = 125

70 + 11t = 125

11t = 125 - 70

11t = 55

t = 55 / 11

t = 5

Therefore, the price of one senior citizen ticket is $10, and the price of one student ticket is $5.

Answer:

x= -5, 2

Step-by-step explanation:

set them equal to each other: \(x^{2}+5x-9=2x+1\)

subtract 2x from both sides: \(x^{2} +3x-9=1\)

subtract 1 from both sides to make it equal to zero: \(x^{2} +3x-10=0\)

find which 2 factors of -10 equal 3: 5 and -2

plug it into: \((x +?)\):  \((x+5) (x -2)\)

set both equations to zero: \(x +5=0\)         \(x-2=0\)

solve:  {x| x=-5, 2}

The vector u does not belong to the null space of matrix A. Therefore No.  

A vector belongs to the null space of a matrix if and only if, when the matrix is multiplied by the vector, the result is the zero vector.

We can test this by multiplying the matrix A with the vector u.

Matrix A×Vector u is;

= \(\left[\begin{array}{cc}-2*2 + 3*4 - 8*1\\-3*2 - 2*4 + 18*1\end{array}\right]\)

= \(\left[\begin{array}{c}0, 4\end{array}\right]\)

As the result is not the zero vector, the vector u does not belong to the null space of matrix A.

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The new coordinates of the two points after rotating the parallel lines 180 degrees clockwise are (2, -7) and (-8, 5).

What are parallel lines?

In geometry, parallel lines can be defined as two lines in the same plane that are at equal distance from each other and never meet.

If the set of parallel lines contains the points (-2, 7) and (8, -5), then the two lines are parallel to each other and have the same slope. We can find the slope of the line that passes through these two points using the slope formula:

slope = (y2 - y1) / (x2 - x1)

slope = (-5 - 7) / (8 - (-2))

slope = -12 / 10

slope = -6 / 5

So, the equations of the two parallel lines are:

y - 7 = (-6 / 5)(x + 2) --- equation 1

y + 5 = (-6 / 5)(x - 8) --- equation 2

To rotate the lines 180 degrees clockwise, we need to negate both the x and y coordinates of the points on the lines. That is, we need to replace each point (x, y) with the point (-x, -y).

So, after the rotation, the new coordinates of the two points will be:

(-(-2), -7) = (2, -7) --- for point (-2, 7)

(-(8), -(-5)) = (-8, 5) --- for point (8, -5)

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Answer:

\(12-[20-2(6^2\div3\times2^2)]=88\)

Step-by-step explanation:

So we have the expression:

\(12-[20-2(6^2\div3\times2^2)]\)

Recall the order of operations or PEMDAS:

P: Operations within parentheses must be done first. On a side note, do parentheses before brackets.

E: Within the parentheses, if exponents are present, do them before all other operations.

M/D: Multiplication and division next, whichever comes first.

A/S: Addition and subtraction next, whichever comes first.

(Note: This is how the order of operations is traditionally taught and how it was to me. If this is different for you, I do apologize. However, the answer should be the same.)

Thus, we should do the operations inside the parentheses first. Therefore:

\(12-[20-2(6^2\div3\times2^2)]\)

The parentheses is:

\((6^2\div3\times2^2)\)

Square the 6 and the 4:

\((36\div3\times4)\)

Do the operations from left to right. 36 divided by 3 is 12. 12 times 4 is 48:

\((36\div3\times4)\\=(12\times4)\\=48\)

Therefore, the original equation is now:

\(12-[20-2(6^2\div3\times2^2)]\\=12- [20-2(48)]\)

Multiply with the brackets:

\(=12-[20-96]\)

Subtract with the brackets:

\(=12-[-76]\)

Two negatives make a positive. Add:

\(=12+76=88\)

Therefore:

\(12-[20-2(6^2\div3\times2^2)]=88\)

The points where the inequality x+ 5y <-30 intercepts is ( 30, 0 ) and (0,6).

Here given the inequality.

x + 5y ≤ 30

To find the x-intercepts.

We have to substitute 0 for y and solve x to determine the x-intercepts.

x + 5 × 0 = 30

By solving the equation.

x = 30

( 30, 0 ) is the x-intercepts.

To find the y-intercepts.

By substituting 0 for x and solving y will get the y-intercept(s).

0 + 5y = 30

5y =30

y = 30/5

y = 6

In the point form, y-intercept.

Y-intercept(s): ( 0, 6 )

(30, 0) is the x-intercept.

Y-intercepts at : ( 0, 6 ).

The points in which the inequality x+ 5y <-30 intercepts is (30, 0) and (0,6).

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Data set with median 12 is 10, 8, 9, 11, 12, 12, 12, 13, 14, 16

and with out 12 is 9, 7, 11, 10, 13, 15, 16, 14, 8, 17

Here are two different data sets with 10 values each, both having a median of 12:

Data Set 1 (Includes 12):

10, 8, 9, 11, 12, 12, 12, 13, 14, 16

The data set contains 10 values, including multiple occurrences of 12. The median is 12 because it is the middle value when the data set is arranged in ascending order.

Data Set 2 (Does Not Include 12):

9, 7, 11, 10, 13, 15, 16, 14, 8, 17

The data set contains 10 values, but none of them are 12.

However, the median is still 12 because it is the value that divides the data set into two equal halves when arranged in ascending order.

In this case, the values on either side of the median would be 11 and 13.

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Answer:

24.5 inches need to be cut

Step-by-step explanation:

The length of the rectangular garden is 23 feet.

Area of a two dimensional shape is the total region which is bounded by the object's shape.

Given that,

Length of the rectangular garden is 5 feet longer than its width.

Let w be the width of the rectangle.

Then w + 5 is the length of the rectangle.

Area of a rectangle = Length × Width

Area is given as 414 square feet.

(w + 5) w = 414

w² + 5w - 414 = 0

Factorizing,

(w - 18) (w + 23) = 0

w - 18 = 0, then w = 18

w + 23 = 0, then w = -23

w = -23 is not possible for the width.

So w = 18 feet

Length of the rectangle = w + 5 = 18 + 5 = 23 feet

Hence 23 feet is the length of the rectangle.

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Answer:

A

Step-by-step explanation:

4x+2y=8

2y=-4x+8

y=-2x+4

sorry if this wasn't in time

Answer:

B. y-5= 4(x-2)

Step-by-step explanation:

I'm not sure how to describe it, believe me tho but if my answer is incorrect my fault then.

Answer: A. y - 5 = 4(x + 2)

\(\rule{130}{1}\)

\(\rule{1}{5 } \ \ \sf point \ slope \ form : y-y_1 = m(x - x_1) \quad \ where \ (x_1 , \ y_1)\ are \ points \ \ \ \rule{1}{5}\)

                                                   Given points: (-2, 5)

solving stepwise:

\(\rightarrow y - 5 = 4(x - (-2))\)

\(\rightarrow y - 5 = 4(x +2) \bf \quad \quad This \ is \ point \ slope \ form\)

\(\rightarrow y - 5 = 4x + 8\)

\(\rightarrow y = 4x + 13 \quad \quad \quad \quad \bf This \ is \ slope \ intercept \ form\)

y= √x

Identify the equation of the function.

y= √-1+3

Answer:

b. y = square root x

Step-by-step explanation:

In this scenario, we should use a two-sample t-test with unequal variances. The reason for this is because we have two samples with different estimated standard deviations.

A two-sample t-test is appropriate because we are comparing two independent samples. The t-test assumes that the populations are normally distributed, and since we believe that both populations are normally distributed, this assumption is met. Additionally, the unequal variances in the samples suggest that we should use a two-sample t-test with unequal variances, which takes into account the differences in standard deviations between the two populations. In summary, we should use a two-sample t-test with unequal variances to compare the two populations based on the provided information.

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Answer:

okay the first best step is to subtract 100 from both side the second best step is to divide 15 by both side