A die is rolled 260 times. Predict how many times it will show a 3 or a 5.

A. about 43
B. about 65
C. about 87
D. about 130
E. about 173

The answer to the given question is option c) The blocks in this design are the four different litters.

In a block design, the experimental units are grouped into homogeneous sets or blocks based on one or more characteristics that are expected to affect the response variable. The purpose of blocking is to reduce the variability of the response variable by reducing the differences between the experimental units within each block. In this experiment, the four different litters are the blocks. The pigs within each litter are expected to be more similar to each other than to pigs from other litters, so the blocks will reduce the variability of the response variable (e.g. weight gain, feed consumption) by accounting for the differences between the litters. The three different dietary supplements are the treatments that are being compared, and the 24 identical pens are the locations where the treatments are applied.

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The statements that represent the scenario are

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

Friends = 5

Amount by each = 10

This means that

The total cost is

c / 5 < 10

The inequality is less than

So, the number line would be shaded to the left of the maximum value.

Also

The total cost of the food could be $40.

This is because 40 is less than 50

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Question

Five friends ate in a restaurant together and split the cost, c, equally. Each person paid less than $10. Which statements represent the scenario? Check all that apply.

A. The situation can be represented using the inequality c ÷ 5 < 10.

B. The total cost of the food could be $40.

C. When graphed, the number line would be shaded to the left of the maximum value.

D. The total cost of the food could be $50.

The age of “Old Fred” is approximately 487.6 years old.

We are given that;

Thickness=0.5cm

Circumference=766cm

Now,

To estimate the age of “Old Fred”, we can use the formula:

Age=Circumference​/π×Average ring thickness

Note that this is only an estimate based on the average ring thickness. The actual age of the tree may vary depending on the environmental factors that affect its growth.

Plugging in the given values, we get:

Age=π×0.5766​≈487.6

Therefore, by the given circumference the answer will be 487.6 years old.

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Answer:2

Step-by-step explanation:

2

Answer:

The formula for the volume of a cone is ⅓ r2h cubic units, where r is the radius of the circular base and h is the height of the cone.The volume of any sphere is 2/3rd of the volume of any cylinder with equivalent radius and height equal to the diameter.The formula for the volume of a sphere is 4⁄3πr³. For a cylinder, the formula is πr²h. A cone is ⅓ the volume of a cylinder, or 1⁄3πr²h

Step-by-step explanation:

The formula for volume is: Volume = length x width x height

Answer:

Step-by-step explanation:

Volume of a sphere:  4/3 π r³

4/3 (3.14) (2.5)³ =

4/3 (3.14) (15.625) = 65.42 units³

Volume of a cylinder = π r² h

(3.14) (2.5)² (4)

(3.14) (6.25)(4) = 78.5 units²

Volume of a Cone = 1/3 π r² h

(1/3)(3.14)(2.5)²(4) =

(1/3)(3.14)(6.25)(4) = 26.17 units²

Refer to the photo taken. Comment any questions you may have.

Answer:

D) x=60

The choose

Step-by-step explanation:

360 =70+70+50+50+2x

360=240+2x

360-240=2x

120=2x

x=120/2

x=60

Answer:

3x+2=1

-3x=1

-x+⅓=⅔

-x+1=2x+2

3x=-1

according to the question

given data in the question,

the foci of an ellipse are (5,0) and (-5,0)

and vertices are (8,0) and (-8,0)

** Standard Form of an Equation of an Ellipse is  

where Pt (h k) is the center. (a variable positioned to correspond with major axis)

a and b  are the respective vertices distances from center

and  are the foci distances from center: a > b

Recommend sketching it...Foci (-5,0) (5,0) and Vertices (8,0) (-8,0).

then using √(64+b^2  )=5 to find b

64 - b^2 = 25, b = √ 39

**** The standard form of the equation is an ellipse

where Pt (h, k) is the center. (variable aligned to match long axis)

a and b are the respective vertex distances from the center.

and   are the distances from the center to the focal point.

a > b

hyperbolic equations in normal form,

C (h, k) and 2b units up and down from the centre at vertex 'b' Horizontal axis length

Focus units up and down from the center along x = h

& asymptotes straight line through C (h, k) with slope m = b/a

after that.

C (h, k) and corner 'a' are units left and right of the center, 2a is the length of the horizontal axis

The focal points are units left and right of the center along y = k.

asymptotes straight line through C (h, k) with slope m = b/a

parabolic vertex form open to the top (a>0) or bottom (a<0 x=removed>0) or left (a<0),

where (h, k) is the vertex and y = k is the line of symmetry.

The standard form is where the focus is (h + p, k )

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** Standard Form of an Equation of an Ellipse is  

where Pt (h k) is the center. (a variable positioned to correspond with major axis)

a and b  are the respective vertices distances from center

and  are the foci distances from center: a > b

Recommend sketching it...Foci (-5,0) (5,0) and Vertices (8,0) (-8,0).

then using √(64+b^2  )=5 to find b

64 - b^2 = 25, b = √ 39

**** The standard form of the equation is an ellipse

where Pt (h, k) is the center. (variable aligned to match long axis)

a and b are the respective vertex distances from the center.

and   are the distances from the center to the focal point.

a > b

hyperbolic equations in normal form,

C (h, k) and 2b units up and down from the center at vertex 'b' Horizontal axis length

Focus units up and down from the center along x = h

& asymptotes straight line through C (h, k) with slope m = b/a

after that.

C (h, k) and corner 'a' are units left and right of the center, 2a is the length of the horizontal axis

The focal points are units left and right of the center along y = k.

asymptotes straight line through C (h, k) with slope m = b/a

parabolic vertex form open to the top (a>0) or bottom (a<0 x=removed>0) or left (a<0),

where (h, k) is the vertex and y = k is the line of symmetry.

The standard form is where the focus is (h + p, k )

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The equation of the ellipse with foci as (5,0) and (-5,0) is

\(\frac{x^2}{49}+\frac{y^2}{24}=1\)

A plane section of a right circular cone that is a closed curve is produced by a point moving in such a way that the sum of its distances from two fixed points is a constant.

Ax2 + Bxy + Cy2 + Dx + Ey + F = 0 is the equation in standard form for a conic section. Here, A, B, C, D, E, and F are all real integers, and A 0, B 0, and C 0. The conic section is an ellipse if B2 - 4AC 0.

where the center is Pt(h,k). (a variable placed such that it lines up with the main axis)

The relative vertices' distances from the center are a and b.

the foci's separations from the center are: a > b

It's suggested that you sketch it: Vertices (-7,0), Focus (-5,0), and (5,0). (7,0).

then finding b 

 when 49 - b2 = 25.

The relative vertices' distances from the center are a and b.

furthermore, 

the foci's separations from the center are: a > b

The equation for an opening up and down hyperbola

 having C(h,k), vertices "b" units up and down from the center, and a transverse axis length of 2b.

Foci

29 units away from the center, along x = h

& Asymptotes Lines Through C(h,k), Slope m = b/a

Equation of a Hyperbola Opening Right and Left Standard Form:

with C(h,k), vertices 'a' units to the right and left of the center, and 2a the transverse axis length

y = k along 29 units to the right and left of the center

& Asymptotes Lines through C(h,k), slopes m = b/a

 is the vertex form of a Parabola with an opening up (a>0) or down (a0).

where the vertex is (h,k), and the line of symmetry is (x = h).

The conventional form is  with (h,k + p) as the main focus.

the vertex form of a Parabola opening right(a>0) or left(a0).

where y = k is the Line of Symmetry and (h,k) is the vertex

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Step-by-step explanation:

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Answer:

C) 5

Step-by-step explanation:

\(f(x)=x^2-3x+5\)

\(f(0)=(0)^2-3(0)+5\)

\(f(0)=0-0+5\)

\(f(0)=5\)

Answer:

1. f(4) or f(n)= 28

2. f(-2) or f(n)= -2

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Step-by-step explanation:

n=4                           n=-2

f(n)= 5(n)+8              f(n)= 5(n)+8

f(n)= 5(4)+8              f(n)= 5(-2)+8

(n)= 20+8                 f(n)= -10+8

f(n)=28                      f(n)=-2

Answer:

Step-by-step explanation:

(a)

Let λ be an eigenvalue of A, and let x be the corresponding eigenvector. Then we have Ax = λx. Consider the matrix B = A - λI, where I is the identity matrix. We want to show that B has rank at least m-1.

Since A is tridiagonal, it follows that B is also tridiagonal. Moreover, since A is Hermitian, it follows that B is also Hermitian. Thus, B has the following form:

B = [b1 c1 ]

[a2 b2 c2 ]

[ a3 b3 c3 ]

[ . . ]

[ . cm-1 bm-1 cm]

where bi = ai - λ, for i = 1, 2, ..., m.

Now, let y be the vector obtained by setting the first entry of x to zero, i.e., y = [0 x2 x3 ... xm]T. Then we have By = Ax - λx = 0, since x is an eigenvector of A. It follows that y is in the nullspace of B.

Let z be a vector obtained by setting the second entry of x to zero, i.e., z = [x1 0 x3 ... xm]T. Then we have Bz = [b1 a2 0 ... 0]T, which is nonzero since bi is nonzero for all i. It follows that z is not in the nullspace of B.

Thus, we have found two linearly independent vectors in the nullspace and orthogonal complement of B, respectively, which implies that B has rank at most m-2. Since B is a square matrix of size m, it follows that B has rank at least m-1. Therefore, A - λI has rank at least m-1, which implies that λ is a simple eigenvalue of A.

(b)

Consider the matrix

A = [1 1 0]

[1 1 1]

[0 1 1]

which is upper-Hessenberg with all subdiagonal entries nonzero. The characteristic polynomial of A is given by

p(λ) = det(A - λI) = (1 - λ)(1 - λ)(1 - λ) - 1 = (λ - 2)λ(λ - 2).

Thus, the eigenvalues of A are λ = 0, 2, 2. Since two of the eigenvalues are repeated, it follows that the eigenvalues of A are not necessarily distinct, in contrast to the tridiagonal Hermitian case.

Answer:  The Real answers are 1) ✔ skewed left and 2) ✔ 1-3

Step-by-step explanation:

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I need 3 more to move to a higher level but

i'm just glad to help.

The work required to pump the water out of the spout is approximately 3,281,270 Joules.

The potential energy of the water in the tank is given by the formula PE = mgh, where m is the mass of the water, g is the acceleration due to gravity, and h is the height of the water above the spout.

Since the tank is spherical, the height of the water above the spout can be found by subtracting the length of the spout from the radius of the tank: h = 9 - 3 = 6 meters.

The mass of the water can be found using its density, which is 1000 kg/m^3: m = (4/3)πr^3ρ = (4/3)π(9^3)(1000) = 305,362 kg. Substituting these values into the formula for potential energy gives PE = (305,362)(9.8)(6) = 17,899,947 Joules.

However, since the question is asking for the work required to pump the water out, we need to subtract the work done by gravity as the water exits the spout. The work done by gravity is given by W = mgh, where h is the height of the spout above the ground (which we assume is the same as the height of the water above the spout).

Substituting the values we already calculated gives W = (305,362)(9.8)(3) = 8,933,952 Joules. Therefore, the work required to pump the water out of the spout is approximately 17,899,947 - 8,933,952 = 3,281,270 Joules.

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The work (in Joules) required to pump the water out of a spout that extends 3 meters out from the top of the tank is 147,249 Joules

To find the work required to pump the water out of the spout, we need to calculate the gravitational potential energy of the water.

The formula for gravitational potential energy is given by:

Potential Energy = mass * gravitational acceleration * height

In this case, the mass of the water is equal to its volume multiplied by its density. The volume of the water can be calculated as the volume of the spherical segment formed by the tank and the spout.

The volume of the spherical segment can be calculated using the formula:

V = (1/6)πh(3a^2 + h^2)

where h is the height of the segment (3 m in this case) and a is the radius of the base of the segment (9 m in this case).

The mass of the water is then:

mass = density * volume

Substituting the given values:

mass = 1000 kg/m^3 * [(1/6)π(3)(9^2 + 3^2)]

Next, we can calculate the potential energy using the formula:

Potential Energy = mass * gravitational acceleration * height

Potential Energy = mass * 9.8 m/s^2 * 3 m

Finally, round the answer to the nearest whole number since we are asked to provide the answer in Joules.

Performing the calculations, the work required to pump the water out of the spout is approximately 147,249 Joules.

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Answer:

\( {h =}^{2} = {p}^{2} \: + {b}^{2} \)

\( {h}^{2} = {16}^{2} + {12}^{2} \)

\( {h}^{2} = 256 + 144\)

\(h = \sqrt{400} \)

\(h = 20\)

therefore the length of the ladder is 20ft

Answer:

1350m

Step-by-step explanation:

Let the distance ran by Denise, Farah and Elaine be D, F and E meters respectively.

From the given information,

D= ⅔(E +F) -----(1)

E= ½(D +F) -----(2)

Let's get rid of the fraction so the equations are much easier to work with.

From (1):

3D= 2(E +F) (Multiply both sides by 3)

3D= 2E +2F -----(3) (Expand)

From (2):

2E= D +F -----(4)

Substitute (4) into (3):

3D= D +F +2F

3D -D= 3F

2D= 3F

Given that Farah ran 360m, F= 360.

2D= 3(360)

2D= 1080

D= 1080 ÷2

D= 540

2E= D +F

2E= 540 +360

2E= 900

E= 900 ÷2

E= 450

Total distance the 3 girls ran

= D +F +E

= 540 +360 +450

= 1350m

Alternatively, you could start by substituting F= 360 to equations (1) and (2).

Take two points

Slope:-

\(\\ \sf\longmapsto m=\dfrac{50-40}{1}=10\)

Equation in point slope form

\(\\ \sf\longmapsto y-40=10(x-4)\)

\(\\ \sf\longmapsto y=10x\)

Or

Answer:

Take two points(4,40)(5,50)Slope:-Equation in point slope formOrf(x)=10x

Step-by-step explanation:

The set we get from the universal set,

1.(O∪R)'= {25,27}

2.O∩R={Φ}

3.(O∩R)'= {22,23,24,25,26,27,28,29,30}

Given that,

The set are U={22,23,24,25,26,27,28,29,30}

O={prime number}={23,29}

R={even numbers}={22,24,26,28,30}

We have to find (O∪R)',(O∩R)' and O∩R

A set is a clearly defined group of things in mathematics. Set names and symbols begin with a capital letter. According to set theory, a set's constituent elements can be anything, including people, alphabetic letters, numbers, shapes, variables, etc.

First,

O∪R= {23,29}∪{22,24,26,28,30}

O∪R= {22,23,24,26,28,29,30}

Now,

1. (O∪R)'=U-(O∪R)

(O∪R)'= {22,23,24,25,26,27,28,29,30} - {22,23,24,26,28,29,30}

(O∪R)'= {25,27}

2. O∩R={23,29}∩{22,24,26,28,30}

O∩R={Φ}

3. (O∩R)'=U-(O∩R)

(O∩R)'= {22,23,24,25,26,27,28,29,30} -{Φ}

(O∩R)'= {22,23,24,25,26,27,28,29,30}

Therefore, The set we get from the universal set,

1.(O∪R)'= {25,27}

2.O∩R={Φ}

3.(O∩R)'= {22,23,24,25,26,27,28,29,30}

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Answer:

Option "A" is the correct answer.

Number of truck and car in parking is 64 , 80

Step-by-step explanation:

Given:

Sample ratio = 4 truck and 5 car

Find:

Number of truck and car in parking

Computation:

Sample ratio = 4 / 5

So,

Option 1

64 truck 80 cars

ratio = 64 / 80

ratio = 4 / 5

Option 2

72 truck 73 cars

ratio = 72 / 73

84 trucks 100 cars

ratio = 84 / 100

ratio = 21 / 25

96 truck 110

ratio = 96 / 110

ratio = 48 / 55

sample ratio match with option 1

So,

Number of truck and car in parking is 64 , 80

x = k/2 + 11/2

Step-by-step explanation:

\(\frac{k}{2} + \frac{11}{2} = \frac{k+11}{2}\)

hope this helped :)

Answer:

y=x-1

Step-by-step explanation:

The equation is currently in standard form which is a+b=y and slope-intercept is y=mx+b where m is the slope and b is the y-intercept. To change the form we must move the terms around using Properties of Equality.

First, subtract 1 from both sides

x-y-1=1-1

x-y-1=0

Then, add y to both sides

x-y-1+y=0+y

x-1=y

So that is the equation in slope-intercept form with a slope of 1 and a y-intercept of -1.

Answer:

y=x-1

Step-by-step explanation:

It is y=x-1 because first when we do ANYTHING first. We leave the y on the left side of the equation, since the slope y=mx+b has the y always on the left side. So we subtract x from both sides and we get -y=-x+1. We are NOT DONE yet, so after this, we divide both sides by -1. Why? This is because you cannot have a negative y. Dividing both sides by -1 you finally get y=x-1. If this is trouble some to read, I will also put how to solve the problem down below. :)

Let's solve for y.

x−y=1

Step 1: Add -x to both sides.

x−y=1+−x

−x

−y=−x+1

Step 2: Divide both sides by -1.

−y/ −1 = −x+1 /−1

y=x−1

Answer:

y=x−1

Answer:

6

Step-by-step explanation:

2x+2y=2*(-2)+2*5=6

Answer:

6

Step-by-step explanation:

Substitute x = - 2, y = 5 into the expression

2x + 2y

= 2(- 2) + 2(5)

= - 4 + 10

= 6

The residual if you know the actual number is 3 and the predicted value is 1.6l is 1.4.

The residual is a measure of the difference between the predicted value and the actual value. In this case, the actual number is 3, and the predicted value is 1.6. To find the residual, we subtract the predicted value from the actual value:

Residual = Actual Value - Predicted Value

= 3 - 1.6

= 1.4

Therefore, the residual in this case is 1.4.

The residual represents the error or the amount by which the predicted value differs from the actual value.

A positive residual indicates that the predicted value is lower than the actual value, while a negative residual indicates that the predicted value is higher than the actual value.

In this case, the positive residual of 1.4 indicates that the predicted value of 1.6 underestimates the actual value of 3 by 1.4.

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Answer:

I think you need to multiply to get the answer, since there's a keyword that it's "per"

Step-by-step explanation:

Divide and then Multiply

8/9 = 0,8

0,8 x 8 = 6,4

(I think that's the answer, hope I helped you)

A minimum of three data points is required to find a single quadratic model for a data set.

A quadratic model is represented by an equation of the form y = ax² + bx + c, where a, b, and c are coefficients. This model has three parameters that need to be determined in order to fit the data accurately.

To uniquely determine the values of a, b, and c, we need three independent equations. Each data point provides one equation, with the x and y values substituted into the quadratic equation. These equations form a system of three equations that can be solved simultaneously to find the coefficients.

Having fewer than three data points would result in an underdetermined system, meaning there would be more than one possible solution for the coefficients. Therefore, at least three data points are needed to find a single quadratic model that best fits the data.

A minimum of three data points is required to find a single quadratic model for a data set.

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