determine intervals when the graph is concave up or concave down

Work Shown:

r = 6 = radius

V = volume of a sphere of radius r

V = (4/3)*pi*r^3

V = (4/3)*pi*6^3

V = 904.77868423386

V = 904.8

I used my calculator's stored version of pi (instead of something like pi = 3.14)

The units "cubic meters" can be abbreviated to m^3 or \(m^3\)

The volume of the given sphere is 904.8 cubic meters. Thus, option B is the answer.

         The volume of a sphere can be calculated using the formula:

V = \(4/3 * \pi * r^3\),

Where V is the volume and r is the radius of the sphere.

\(\pi\) = 3.14

The radius of the sphere (r) = 6m

Plugging in the given radius of 6m into the formula, we get:

V = (4/3) * \(\pi\) * (6^3)

V = 1.333 * \(\pi\) * 216

V = 1.333 * 3.14 * 216

V = 4.1866 * 216

V = 904.8 cubic meters

Therefore, when the radius of the sphere is 6m, the volume of the sphere is 904.8  cubic meters.

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\(\huge \boxed{\sf 8+4\sqrt{5} }\\\\\\\sf Using\ the\ distance\ formula \\\\\displaystyle d = \sqrt{(x_2 - x_1)^2 + (y_2-y_1)^2}\)

\(\sf A(0,4)\ and\ B(2,0)\\\\d = \sqrt{(2 - 0)^2 + (0-4)^2}=2\sqrt{5} \\\\B(2,0)\ and\ C(2,-2)\\\\d = \sqrt{(2 - 2)^2 + (-2-0)^2}=2 \\\\C(2,-2)\ and\ D(0,-2)\\\\d = \sqrt{(0 - 2)^2 + (-2-(-2))^2}=2 \\\\D(0,-2)\ and\ E(-2,2)\\\\d = \sqrt{(-2 - 0)^2 + (2-(-2))^2}=2\sqrt{5} \\\\E(-2,2)\ and\ F(-2,4)\\\\d = \sqrt{(-2 - (-2))^2 + (4-2)^2}=2\\\\F(-2,4)\ and\ A(0,4)\\\\ d=\sqrt{(0-(-2))^2+(4-4)^2} =2\)

\(\sf Adding\ all\ the\ distances \\\\2\sqrt{5} +2+2+2\sqrt{5}+2+2 =8+4\sqrt{5} =16.94427190...\)

Answer:

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

Four of the segments are horizontal or vertical with the length of 2 units:

Two of the segments have same length (parallel segments) with 4 units vertical and 2 units horizontal difference of coordinates:

The perimeter is:

The solution is, given below., as Corresponding Angles in the diagram given are:

<1 and <3

<2 and <4

<5 and <7

<6 and <8

In Plane Geometry, a figure which is formed by two rays or lines that shares a common endpoint is called an angle. The two rays are called the sides of an angle, and the common endpoint is called the vertex.

here, we have,

a. A transversal is a line that intercepts two straight lines.

Line N is a transversal

b. Corresponding Angles are found lying in the same corresponding corners.

Corresponding Angles in the diagram given are:

<1 and <3

<2 and <4

<5 and <7

<6 and <8

c. Alternate interior angels are located within the 2 lines intersected by the transversal, and they are found alternating both sides of the transversal.

Alternate interior angles are:

<2 and <7

<3 and <6

d. Alternate exterior angles lie outside the two lines cut across by the transversal and they alternate each other along the transversal. They include:

<1 and <8

<4 and <5

e. Consecutive interior angles lie on the the same side of the transversal and are found within the two lines cut across by the transversal. They are:

<2 and <3

<6 and <7

f. Consecutive exterior angles are found outside the two lines cut across by the transversal and are on the same side of the transversal. They are:

<1 and 4

<5 and <8

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Answer: he payed for 9 months

Step-by-step explanation:

500-140= 360      and 360 divided by 40 is 9

Answer:

AB = 37

Step-by-step explanation:

as opposite sides in a parallelogram are equal we know that 6x-10 = 2x+18

therefore when we simplify

6x-10 = 2x+18          add 10 to both sides

6x = 2x+28              take 2x from both sides

4x = 28                    divide both sides by 4

x = 7

therefore as x = 7 you can substitute x in

6x - 10

6(7) - 10

47 - 10

37

(a) To find the probability that at least two children have blue eyes, given that at least one child has blue eyes, we need to consider the possible combinations of blue-eyed children in the family of 3 children.

Let's break it down step by step:

1. Find the total number of possible outcomes when 3 children are considered. Each child can have either blue eyes (B) or non-blue eyes (N). So, the total number of outcomes is 2^3 = 8.

2. Now, let's determine the outcomes where at least one child has blue eyes. This can be achieved by finding the outcomes where no child has non-blue eyes (NNN) and subtracting it from the total number of outcomes.

  The outcomes where no child has non-blue eyes are NNN, NNB, NBN, and BNN (4 outcomes).

  So, the number of outcomes where at least one child has blue eyes is 8 - 4 = 4.

3. Next, we need to find the outcomes where at least two children have blue eyes. These outcomes can be BBB, BBN, BNB, and NBB (4 outcomes).

4. Finally, we calculate the probability by dividing the number of outcomes where at least two children have blue eyes by the number of outcomes where at least one child has blue eyes.

  Probability = Number of outcomes where at least two children have blue eyes / Number of outcomes where at least one child has blue eyes

  Probability = 4 / 4 = 1

Therefore, the probability that at least two children have blue eyes, given that at least one child has blue eyes, is 1.

(b) To find the probability that at least two children have blue eyes, given that the youngest child has blue eyes, we can follow a similar approach as in part (a).

1. Find the total number of possible outcomes when 3 children are considered. Each child can have either blue eyes (B) or non-blue eyes (N). So, the total number of outcomes is 2^3 = 8.

2. Since we know that the youngest child has blue eyes, we only need to consider the outcomes where the youngest child has blue eyes (BNB, BBB) and subtract it from the total number of outcomes.

  The outcomes where the youngest child has blue eyes are BNB and BBB (2 outcomes).

  So, the number of outcomes where at least one child has blue eyes is 8 - 2 = 6.

3. Next, we need to find the outcomes where at least two children have blue eyes. These outcomes can be BBB and BNB (2 outcomes).

4. Finally, we calculate the probability by dividing the number of outcomes where at least two children have blue eyes by the number of outcomes where at least one child has blue eyes.

  Probability = Number of outcomes where at least two children have blue eyes / Number of outcomes where at least one child has blue eyes

  Probability = 2 / 6 = 1/3

Therefore, the probability that at least two children have blue eyes, given that the youngest child has blue eyes, is 1/3.

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The dual linear program for the given primal linear program is:

Maximize: y1 + 5y2

Subject to:

2y1 + 3y2 ≤ 1

y1 + 2y2 ≤ -1

-3y1 - y2 ≤ 0

y1, y2 unrestricted.

To find the dual of the given linear program, we need to follow these steps:

Step 1: Write the primal linear program in standard form.

Primal Linear Program:

Minimize: x1 - x2

Subject to:

2x1 + x2 - 3x3 = 1

3x1 + 2x2 - x3 = 5

x1, x2, x3 unrestricted

Step 2: Introduce the dual variables.

Let y1 and y2 be the dual variables corresponding to the two constraints in the primal linear program.

Step 3: Write the dual linear program.

Dual Linear Program:

Maximize: y1 + 5y2

Subject to:

2y1 + 3y2 ≤ 1

y1 + 2y2 ≤ -1

-3y1 - y2 ≤ 0

y1, y2 unrestricted

The dual linear program is obtained by switching the objective function from minimization to maximization and reversing the direction of the inequalities in the constraints.

The dual linear program for the given primal linear program is:

Maximize: y1 + 5y2

Subject to:

2y1 + 3y2 ≤ 1

y1 + 2y2 ≤ -1

-3y1 - y2 ≤ 0

y1, y2 unrestricted.

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Answer:

a)A=53

b)A=42.68

c)A=60

To dilate a rectangle by 2 , multiplied by the scale factor with every coordinates of rectangle

Assume that, the origin (0, 0) be the center of dilation in the coordinate plane.

Let ABCD be a Rectangle in the coordinate plane. The points in the coordinate planes are A(-2, 2), B(3, 2), C(3, -2), D(-2, -2)

We have to dilate by scale factor 2, then every coordinate point of the original triangle will multiplied by the scale factor

Coordinates of new rectangles : A'(-4,4) , B'( 6, 4) ,C(6, -4) and D'(-4,  -4)

Therefore, When we dilate a rectangle by scale factor 2 ,

The dilated triangle will be A’B’C’D’ and the coordinate points obtained are  A'(-4,4) , B'( 6, 4) ,C(6, -4) and D'(-4,  -4)

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Answer:

The answer is x>17

Step-by-step explanation:

First subtract 4x from both sides

6x - 8 > 4x + 26

-4x. -4x

2x - 8 > 26

8 is negative so to get rid of it add 8 to -8 and 26

2x - 8 > 26

+8. +8

2x > 34

x needs to be by itself so divide both sides by 2

2x > 34

2. 2

x > 17

Answer:%

Step-by-step explanation:

Answer:

To find a a fraction of a whole number, you multiply the numerator of the fraction by the given number and then divide the product by the denominator of the fraction

Solved example for finding a fraction of a whole number:

1)

Find 1/3 of 21.

To find 1/3 of 21, we multiply the numerator 1 by the given whole number 21 and then divide the product 21 by the denominator 3.

1/3 × 21 = 1 × 21/3 = 21/3 = 7

So, 1/3 of 21 = 7.

1/3 of 21 is 7

Answer:

For finding a fraction of a whole number, we multiply the numerator of the fraction by the given number and then divide the product by the denominator of the fraction.

Examples for finding a fraction of a whole number:

Find 1/3 of 21.

To find 1/3 of 21, we multiply the numerator 1 by the given whole number 21 and then divide the product 21 by the denominator 3.

1/3 × 21 = 1 × 21/3 = 21/3 = 7

So, 1/3 of 21 = 7.

Here are some more examples

Step-by-step explanation:

Find 2/5 of 15.

To find 2/5 of 15, we multiply the numerator 2 by the given whole number 15 and then divide the product 30 by the denominator 5.

2/5 × 15 = 2 × 15/5 = 30/5 = 6

So, 2/5 of 15 = 6.

Find 3/8 of 48.

To find 3/8 of 48, we multiply the numerator 3 by the given whole number 48 and then divide the product 144 by the denominator 8.

3/8 × 48 = 3 × 48/8 = 144/8 = 18

So, 3/8 of 48 = 18.

Answer:

Because the P-value of 0.0733 > , Lucy should fail to reject H0. There is not convincing evidence that the proportion of customers who will ask for a straw is less than 50%.

The volume of the solid is 4,503.22 in³.

What is volume?

A volume is simply defined as the amount of space occupied by any three-dimensional solid. These solids can be a cube, a cuboid, a cone, a cylinder, or a sphere. Different shapes have different volumes

The volume of a solid with a hollow cylinder can be calculated by subtracting the volume of the inner cylinder from the volume of the outer cylinder.

Assuming the dimensions in the figure are in inches, the outer cylinder has a height of 17 inches and a radius of 9 inches, so its volume is:

\(V_{outer} = \pi * r^2 * h\)

= π × 9² × 17 ≈ 4,842.51 in³

The inner cylinder has a height of 12 inches and a radius of 3 inches, so its volume is:

\(V_{inner} = \pi * r^2 * h\) = π × 3² × 12 ≈ 339.29 in³

To find the volume of the solid, we need to subtract the volume of the inner cylinder from the volume of the outer cylinder:

\(V_{solid }= V_{outer} - V_{inner}\)

≈ 4,842.51 - 339.29 ≈ 4,503.22 in³

Hence, the volume of the solid is 4,503.22 in³.

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Answer:

PT = 17

Step-by-step explanation:

Since T is the midpoint of PQ, then

PT = TQ , substitute values

4x + 5 = 8x - 7 ( subtract 4x from both sides )

5 = 4x - 7 ( add 7 to both sides )

12 = 4x ( divide both sides by 4 )

3 = x

Thus

PT = 4x + 5 = 4(3) + 5 = 12 + 5 = 17

Answer:

17

Step-by-step explanation:

since T is mid point of PQ

PT=TQ

\(4x + 5 = 8x - 7 \\ 5 + 7 = 8x - 4x \\ 12 = 4x \\ x = 12 \div 4 \\ x = 3 \\ \)

so

\(pt = 4x + 5 \\ = 4(3) + 5 \\ = 12 + 5 \\ pt = 17\)

Answer:

Step-by-step explanation:

Area of rectangle = length * width

                             = 6 *5

                             = 30 sq.ft

Area of triangle1 = \(\frac{1}{2}*base*height\)

                           \(= \dfrac{1}{2}*5 * 3\\\\= \dfrac{15}{2}\\\\= 7.5 \ ft^{2}\)

\(Area \ of \ triangle2 = \dfrac{1}{2}*4*2\\= 4 \ ft^{2}\)

Area of figure = 30 + 7.5 + 4 = 41.5 sq.ft

Answer:

\(m = \frac{96-3 }{5-0}\)

remember: slope is Δy/Δx :)

\(m = \frac{y_{1} - y_{2} }{x_{1} - x_{2}}\)

\(m = \frac{96-3 }{5-0}\)

\(m = \frac{93 }{5}\)

The exponent "product rule" tells somebody/you that, when multiplying two powers that have the same base, you can add the exponents.

Have a good day! ``)

The probability that the molecules will have a total energy of 6 kJ is 1/9 or approximately 0.111.

To find the probability that the two indistinguishable molecules will have a total energy of 6 kJ, we need to consider all the possible energy level combinations they can occupy.
There are a total of 3 possible energy levels for each molecule, which means there are 3 x 3 = 9 possible energy level combinations for the two molecules. We can list these combinations as follows:
- 1 kJ + 1 kJ = 2 kJ
- 1 kJ + 2 kJ = 3 kJ
- 1 kJ + 3 kJ = 4 kJ
- 2 kJ + 1 kJ = 3 kJ
- 2 kJ + 2 kJ = 4 kJ
- 2 kJ + 3 kJ = 5 kJ
- 3 kJ + 1 kJ = 4 kJ
- 3 kJ + 2 kJ = 5 kJ
- 3 kJ + 3 kJ = 6 kJ
Out of these 9 possible combinations, only one combination has a total energy of 6 kJ, which is the last one in the list. Therefore, the probability that the probability will have a total energy of 6 kJ is 1/9 or approximately 0.111.
This calculation is based on the assumption that each energy level is equally likely to be occupied by each molecule. If there are any other factors that affect the probability of probability each energy level, the calculation may be different.

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The zeros of the function represent the prices at which the taco food truck breaks even or has zero profity and the zeros of the function are x = 5 + √2 and x = 5 - √2.

To find the zeros of the function y = -6(x-5)^2 + 12, we need to set y equal to zero and solve for x:

0 = -6(x-5)^2 + 12

Let's solve this equation:

6(x-5)^2 = 12

Dividing both sides by 6:

(x-5)^2 = 2

Taking the square root of both sides:

x - 5 = ±√2

Adding 5 to both sides:

x = 5 ± √2

Therefore, the zeros of the function are x = 5 + √2 and x = 5 - √2.

Now let's interpret these zeros. In this context, the variable x represents the price of a taco. The zero points represent the prices at which the taco food truck will have zero profit or break even.

x = 5 + √2: This zero means that if the taco price is set at 5 + √2 dollars, the daily profit of the food truck will be zero. In other words, if the taco is priced slightly above 5 dollars plus the square root of 2, the food truck will not make any profit.

x = 5 - √2: This zero means that if the taco price is set at 5 - √2 dollars, the daily profit of the food truck will be zero. In other words, if the taco is priced slightly below 5 dollars minus the square root of 2, the food truck will not make any profit.

In summary, the zeros of the function represent the prices at which the taco food truck breaks even or has zero profit.

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The five dealers included in the sample are: Dealer 02: 05, Dealer 06: 28, Dealer 09: 38, Dealer 03: 08, Dealer 11: 66

To select a random sample of five dealers from the given random numbers, we need to use a method known as random sampling without replacement, which ensures that no dealer is selected more than once.

Here are the steps to select a random sample of five dealers from the given random numbers:

Step 1: List all the dealers using the given random numbers in ascending order.02, 05, 08, 20, 21, 28, 29, 31, 38, 49, 59, 66

Step 2: Assign each dealer a number between 01 and 12. Dealer 01 corresponds to 02, dealer 02 corresponds to 05, dealer 03 corresponds to 08, and so on.

Step 3: Generate five random numbers between 01 and 12 using a random number generator or by drawing numbers from a hat. For instance, let's assume that the five random numbers we get are 02, 06, 09, 03, and 11.02 corresponds to dealer 05, 06 corresponds to dealer 28, 09 corresponds to dealer 38, 03 corresponds to dealer 08, and 11 corresponds to dealer 66.

Therefore, the five dealers included in the sample are: Dealer 02: 05, Dealer 06: 28, Dealer 09: 38, Dealer 03: 08, Dealer 11: 66

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Answer:

12.8% is the answer

Step-by-step explanation:

0.128 x 100

Hey there!

\(\bold{\dfrac{0.128}{1}\times \dfrac{100}{100}}\\\\\bold{Cross\ multiply\downarrow}\\\bold{0.128(100)=12.8}\\\bold{1(100)=100}\\\\\bold{\dfrac{12.8}{100}}}}\\\\\bold{Or\ you\ can\ say\downarrow}\\\\\bold{0.128\times100= \%}\\\\\bold{0.128\times100=12.8\%}}\\\\\\\boxed{\boxed{\bold{Answer: 12.8\%}}}\huge\checkmark\)

Good luck on your assignment and enjoy your day!

~\(\frak{Amphitrite1040:)}\)

Answer:

The slope of RT is: m = 1

Step-by-step explanation:

Given

Determining the slope between (-3, 1) and (2, 6)

\(\mathrm{Slope}=\frac{y_2-y_1}{x_2-x_1}\)

\(\left(x_1,\:y_1\right)=\left(-3,\:1\right),\:\left(x_2,\:y_2\right)=\left(2,\:6\right)\)

\(m=\frac{6-1}{2-\left(-3\right)}\)

Refine

\(m=1\)

Therefore, the slope of RT is: m = 1

Answer:

<S = 151 degrees

<DCE = 52 degrees

Step-by-step explanation:

The sum of interior angle of pentagon is 540 degrees

5x+2+7x-11+13x-31+8x-19+10x-3 = 540

43x - 62= 540

43x = 540+62

43x =602

x = 602/43

x =  14

get <S

<S = 13x-31

<S  = 13(14)-31

<S = 182-31

<S = 151 degrees

2) The sum of interior angle is the exterior

180-7x+2+180-4x-33 = 9x-31

360-11x-31 = 9x - 31

360 = 9x+11x

360 = 20x

x = 360/20

x = 18

<DCE = 180 - 7x - 2

<DCE = 180-7(18)-2

<DCE = 180-126-2

<DCE =  180-128

<DCE = 52 degrees

Answer:

x=3/12 or 1/4

Step-by-step explanation:

x + 1/6 = 5/12

x + 2/12 = 5/12

x = 3/12

converts to 1/4

Answer:

x= 1/4

Step-by-step explanation:

5/12- 1/6 = 1/4

Answer:

A hexagon

Step-by-step explanation:

A hexagon - - - the allen wrench has 2 hexagonal heads. See attached pic.

The geometric shape that forms the hole that fits an allen wrench is a hexagon, which is a six-sided polygon with straight sides and angles.

The geometric shape hexagon-shaped hole in an allen wrench, also known as a hex key, is designed to fit tightly over the hexagonal socket of a screw or bolt head. A hexagon is a six-sided polygon, meaning it has six straight sides and angles. In the case of an allen wrench, the hexagon has internal angles of 120 degrees and opposite sides that are parallel.

The hexagonal shape of the hole in the wrench allows for a tight and secure fit onto the corresponding hexagonal socket of the screw or bolt head. This design ensures that the wrench can apply a significant amount of torque to the fastener without slipping, which is essential for many applications in construction, mechanics, and other industries.

The use of a hexagonal shape also allows for greater precision and control when turning the screw or bolt, making it easier to achieve the desired level of tightness. Overall, the hexagon is an ideal shape for the hole in an allen wrench due to its strength, stability, and precision.

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Lagrange multipliers refer to the method of optimization that is used to find the maximum or minimum value of a function with constraints.

To solve for the critical points of L(x,y,z,λ), we need to find the partial derivatives of L with respect to x, y, z, and\(λ.∂L/∂x = 1 - 2λx = 0∂L/∂y = -1 - 2λy = 0∂L/∂z = 1 - 2λz = 0∂L/∂λ = x² + y² + z² - 2 = 0\)

Solving the first three equations for x, y, and z gives:

x = 1/2λ, y = -1/2λ, z = 1/2λ

Substituting these values into the fourth equation and solving for λ gives:

λ = ±1/√6

Substituting these values back into x, y, and z gives two critical points:

(1/√6, -1/√6, 1/√6) and (-1/√6, 1/√6, -1/√6).

At the critical point (-1/√6, 1/√6, -1/√6), the Hessian matrix is:

H\((L(-1/√6, 1/√6, -1/√6, ±1/√6)) = |-2/√6 0 0 || 0 -2/√6 0 || 0 0 -2/√6 |\)

Since the Hessian matrix is negative definite, this critical point is also a local maximum.

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Answer: 8x^2 + 55x + 42

Step-by-step explanation:

(x+6)(8x+7)=

(8x*x)+(7x)+(6*8x)+(6*7)=

8x^2 + 7x + 48x + 42=8x^2 + 55x + 42

Answer:

x > -5

Step-by-step explanation:

When you divide by a negative number, you must change the sign.

Answer:

explain by giving an example...

Step-by-step explanation:

like suppose lets take x=1...

-2 x 1 < 10

1 < -5

is this right? how can +1 be less than -5...

so it is a wrong equation...

When you divide by a negative number, you must change the sign, or it will give the wrong answer... so here the correct answer should be,

x > -5

To determine the spot price of one Bitcoin, we can use the concept of no-arbitrage pricing. In this case, the futures contract price can be considered as the present value of the expected future spot price, taking into account the risk-free rate.

The futures contract price of $60810 per Bitcoin represents the expected future spot price one year from October 23, 2021. We can calculate the present value of this future price by discounting it at the risk-free rate of 1%. Using the formula for present value, we have:

Present Value = Future Value / (1 + Risk-free rate)

Present Value = $60810 / (1 + 0.01) = $60208.91

Therefore, the spot price of one Bitcoin closest to the given information is approximately $60208, which corresponds to option A.

Insummary, based on the information provided, the spot price of one Bitcoin is closest to $60208 (option A).

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