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The volume common to two spheres, each with radius r, if the distance between their centres is r/2 is V = (11/12)×π×r³.

The attached diagram shows 2 circumferences with radius r and separated centres by r/2.

Let´s call circumferences  1 and 2; by symmetry, rotating area A will produce a volume V₁ identical to a V₂, Obtained by rotating area B ( both around the x-axis), then the whole volume V will be:

V = 2× V₁

V₁ = ∫π×y²×dx         (1)

Now

( x - r/2)²  +  y² = r²       the equation of circumference 1

y² = r² - ( x - r/2)²

Plugging this value in equation (1)

V₁ = ∫π×[  r² - ( x - r/2)²]×dx        with integrations limits    0 ≤ x ≤ r/2

V₁ = π×∫ ( r² - x² + (r/2)² - r×x )×dx

V₁ = π× [  r²×x - x³/3 + (r/2)²×x - (1/2) × r × x²]    evaluate between 0 and r/2

V₁ = π× [(5/4)×r²×x - x³/3 - (1/2) × r × x²]

V₁ =  π× [(5/4)×r² × ( r/2 - 0 ) - (1/3)×(r/2)³ -  (1/2) × r × (r/2)²]

V₁ =  π× [ (5/8)×r³ - r³/24 - r³/8]

V₁ =  π× (11/24)×r³

Then

V = 2× V₁

V = 2×π×11/24)×r³

V = (11/12)×π×r³

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The lengths of the two boards (234 inches and 246 inches) and adding them together, we find that the combined length of the boards is 480 inches.

To find the total length of the two boards, you need to add their individual lengths together.

Step 1: Identify the length of each board. The first board is 234 inches long, and the second board is 246 inches long.

Step 2: Add the lengths of the boards together.

234 (length of first board) + 246 (length of second board) = 480

So, the total length of the two boards on the shelf is 480 inches. This means that if you were to place the two boards end-to-end, they would cover a distance of 480 inches.

In summary, by identifying the lengths of the two boards (234 inches and 246 inches) and adding them together, we find that the combined length of the boards is 480 inches. This calculation helps us understand the total amount of space the boards would occupy if placed side by side.

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Answer:

The answer will be B. V^6

The cube root of the given function is \(x=2\sqrt[3]{2}\).

The given function is x³=16.

Here, the given function can be written as

\(x=\sqrt[3]{16}\)

\(x=\sqrt[3]{2\times2\times2\times2}\)

\(x=\sqrt[3]{2^3\times2}\)

\(x=2\sqrt[3]{2}\)

Therefore, the cube root of the given function is \(x=2\sqrt[3]{2}\).

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"Your question is incomplete, probably the complete question/missing part is:"

How do you solve the cube root function of x³=16.

well, is a quadratic, so it has two roots, in this case that'll be 5 only per se, is really 5 but twice, or we should say it has a root of 5 with multiplicity of 2, that gives us

\(\begin{cases} x = 5 &\implies x -5=0\\ x = 5 &\implies x -5=0\\ \end{cases} \\\\[-0.35em] ~\dotfill\\\\ \stackrel{original~polynomial}{a ( x -5 )( x -5 ) = \stackrel{0}{h}}\hspace{5em}\stackrel{\textit{assuming}}{a=1}\hspace{5em}1(x-5)(x-5)=h(x) \\\\\\ ~\hfill {\Large \begin{array}{llll} x^2-10x+25=h(x) \end{array}}~\hfill\)

Answer:

-8

Step-by-step explanation:

The equation is written in the form y=mx+b, where m is the slope and b is the intercept. So here the intercept is -8.

Micah's boxplot is incorrect because the statistical summary given by his boxplot is inaccurate.

The boxplot is a better at analysing the data as it gives more statistical output of the data than the histogram.

We need to write out the number of times taken by each student,

From the histogram; the data values are :

1, 1, 1, 2, 2, 2, 3, 3, 3, 4, 4, 5, 5, 7, 7, 8, 8, 9, 9, 10, 10, 10

Using a boxplot maker or excel, we could create a boxplot of the data and compare with that given in the question.

5 number summary of Micah's boxplot :

Minimum = 1 (position of lower whisker)

Maximum = 9 (Position of upper whisker)

Lower quartile = 3(starting point of box)

Upper quartile = 8 (endpoint of box)

Median = 5 (vertical line in between box)

Outlier = 10

5 number summary of correct or accurate boxplot :

Minimum = 1 (position of lower whisker)

Maximum = 10 (Position of upper whisker)

Lower quartile = 2 (starting point of box)

Upper quartile = 8.2 (endpoint of box)

Median = 4.5 (vertical line in between box)

Outlier = None

Comparing the box plots, it can be concluded that Micah did not create the boxplot correctly.

Answer:

21,526 people

Step-by-step explanation:

Answer:

r = \(\sqrt{11}\)

Step-by-step explanation:

So we need to complete the square for both parts of the equation

First though we can add the 6 to the other side so we have x² + 2x + y² + 4y = 6

So first we can complete the square for x² + 2x

To do so we need to use \((\frac{b}{2} )^{2}\) to figure out the number we need to add to both sides

In this case our b is 2, so substituting this in we get \((\frac{2}{2} )^{2} =(1)^{2} =1\)

Here we add 1 to both sides and now we have x² + 2x + 1 + y² + 4y = 6 + 1

Now we can follow the same steps to complete the square for y² + 4y

Here our b is 4, so substituting this in we get \((\frac{4}{2} )^{2}=(2)^{2} =4\)

Now we add 4 to both sides and now we have x² + 2x + 1 + y² + 4y + 4 = 6 + 1 + 4

Now condensing everything we have (x + 1)² + (y + 2)² = 11

The formula for a circle is (x - h)² + (y - k)² = r²

In our equation we have r² = 11

To find the radius we need to take the square root of both sides \(\sqrt{r^{2}} =\sqrt{11}\) to get r = \(\sqrt{11}\)

The 23rd term of the sequence is F₂₃ = 2097152.

a) The given sequence of numbers can be calculated using the recursive algorithm below:

Fo= 0,

F₁ = 1,

Fₙ = Fₙ₋₂ + 2

Fₙ₋₁Fₙ₊₁ = FₙFₙ₊₁= [0 1] [0 2] + [1 1] [1 0]

= [1 2] [1 1]

The matrix equation for the general term (Fn) of the sequence is given by:

[Fₙ Fₙ₊₁] = [0 1] [0 2]ⁿ⁻¹ [1 1] [1 0] [F₁₀ F₁₀₊₁]

= [0 1] [0 2]²² [1 1] [1 0] [F₂₂ F₂₂₊₁]

= [0 1] [0 2]²¹ [1 1] [1 0] [1 0] [0 1] [0 2]²¹ [1 1] [1 0] [1 0] [0 1] [0 2]²⁰ [1 1] [1 0] [1 0] [0 1] [2¹⁰ 2¹⁰] [1 1] [1 0] [17711 10946]

The 23rd term of the sequence is given by Fn where n = 23.

Thus, substituting n = 23 into the matrix equation [Fₙ Fₙ₊₁]

= [0 1] [0 2]ⁿ⁻¹ [1 1] [1 0],

We get: [F₂₃ F₂₃₊₁] = [0 1] [0 2]²² [1 1] [1 0] [F₂₃ F₂₃₊₁]

= [0 1] [4194304 2097152] [1 1] [1 0] [F₂₃ F₂₃₊₁]

= [2097152 2097153]

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The probability that exactly 5 out of 10 households in the random sample are wireless-only is approximately 0.2164 or 21.64%.

To find the probability that exactly 5 out of 10 households are wireless-only, we can use the binomial probability formula.

The binomial probability formula is given by:

P(X = k) = (\(^{n}C_k\)) × \(p^k\) × \((1 - p)^{(n - k)\)

Where:

P(X = k) is the probability of exactly k successes

n is the total number of trials

k is the number of desired successes

p is the probability of success in a single trial

In this case, n = 10, k = 5, and p = 0.41 (the probability of a household being wireless-only).

Using the formula, we can calculate the probability:

P(X = 5) = (\(^{10}C_5\)) × \((0.41)^5\) × \((1 - 0.41)^{(10 - 5)\)

Using a combination calculator, we find that (10 C 5) = 252.

P(X = 5) = 252 × \((0.41)^5\) × \((0.59)^5\)

Calculating this expression, we find that P(X = 5) ≈ 0.2164.

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Decision Variables and Objective:

The decision variables in this transportation model are the quantities to be shipped from each plant to each distribution center. Let's denote the quantity shipped from Marietta to Cleveland as X1, from Marietta to Baltimore as X2, and so on. Similarly, let's denote the quantity shipped from Minneapolis to each distribution center as Y1, Y2, and so forth.

The objective of the optimization model is to minimize the total transportation cost. The transportation cost is determined by multiplying the unit cost of shipping between each plant and distribution center by the corresponding quantity shipped and summing up these costs for all combinations.

To enforce the single sourcing constraint, we need to ensure that each distribution center is served from only one plant. This constraint can be represented by adding the following constraint for each distribution center:

X1 + X2 + X3 + X4 = Demand (for each distribution center)

Y1 + Y2 + Y3 + Y4 = Demand (for each distribution center)

These constraints ensure that the total quantity supplied from all plants to a particular distribution center is equal to the demand of that distribution center, effectively enforcing the single sourcing constraint.

Optimization Model and Interpretation of Results:

The optimization model can be formulated as a linear programming problem, where the objective is to minimize the total transportation cost while satisfying the capacity constraints and the single sourcing constraint.

The Excel Solver can be used to solve this model, providing the optimal solution for the decision variables and the corresponding minimum cost.

Interpreting the printouts, we can observe the values of the decision variables X1, X2, X3, X4, Y1, Y2, Y3, Y4, which represent the quantities shipped between each plant and distribution center. Additionally, we can see the total transportation cost, which is the objective value obtained by summing the costs of shipping for all combinations.

Pertinent results could include identifying the optimal shipping quantities that meet customer demand while minimizing costs. Interesting results might include identifying any significant differences in shipping costs between the plants and distribution centers. Unusual results could involve finding a scenario where the total transportation cost does not decrease proportionally with an increase in supply capacity or demand.

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Answer: 3 - 4i

Step-by-step explanation:

For the given polynomial p(x) , if 3 +4i is a root then, 3 - 4i is also the root of p(x).

Consider the given polynomial equation p(x) = 0 It is given that the polynomial P(x) has one root 3 + 4i .

According to complex conjugate theorem,  if V is a polynomial and x + iy is a root of given polynomial then  its conjugate x - iy is also the root of the polynomial.

Thus, for the given polynomial p(x)  if 3 +4i is a root then, 3 - 4i is also the root of p(x).

If a polynomial equation P(x) = 0 has (3 + 4i) as a solution, the other solution it must have (3 - 4i).

What is a polynomial?

Polynomial is formed composed of the phrases Nominal, which means "terms," and Poly, which means "many." An expression that consists of variables, constants, and exponents that is combined using mathematical operations like addition, subtraction, multiplication, and division is referred to as a polynomial.

Conjugate complex numbers are those that only differ in the imaginary part's sign.

a + bi and a - bi, where a and b are real numbers, are generally conjugate, as are, for instance, 2 + 3i and 2 - 3i, -5 - 7i and -5 + 7i, and so on.

Due to the fact that their output is always a genuine number.

The general case is -

= (a + bi)(a - bi)

= a² - abi + abi - (b²)(i²)

= a² + b²

The real example is -

= (2 + 3i)(2 - 3i)

= 2² + 3²

= 4 + 9

= 13

Complex roots for a polynomial equation P(x) = 0 with real coefficients are always represented as conjugate pairs.

So, the following equation must contain (3 - 4i) as a second root if the coefficients are real.

Therefore, P(x) has second root (3 - 4i).

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Answer:

(0.5,0) , (-3,0) ,and (0,-1.5)

Step-by-step explanation:

Just look where the points touch the x- and y-axis.

It touches twice on the x- and once on the y-axis.

Hope that helps!

Answer:

The LCD is 1

Step-by-step explanation:

Answer:

According to exponent rules, when we divide the expressions we ____b. subtract___ the exponents.

I think

Answer:

√61

Step-by-step explanation:

→ Find the distance between y coordinates

2 --4 = 6

→ Find distance between x coordinates

2--3 = 5

→ Find distance

√6² + 5² = √36 + 25 = √61

The maximum number of marks is C. 200 marks with the secured percentage of 40%

How to determine this

A student has to secure 40% marks to pass

i.e 40% of x

=40/100 * x

= 2/5 * x

= 2x/5

Let x represent the total mark

He got 40 and fails by 40 marks

i.e The passing mark = 40 + 40

= 80 marks

To find the maximum mark

2x/5 = 80

Cross multiply

2x = 5 * 80

2x = 400

divides by 2

2x/2 = 400/2

x = 200 marks

Therefore, the maximum marks is 200 marks

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Answer:

18 oatmeal cookies

Step-by-step explanation:

3/4×24=18

Answer:

Here are the answers:

Step-by-step explanation:

1. t=1

2.m=2

3.n=2

4.a=2

5.x=1/3 or 0.3

6.x=15

7.s=4

8.t=2

9.s=1

10.s=3/28, or 0.10714285

11.x=1/3, or 0.3

12.r=2

13.c=-1

14. \(m= \frac{2}{n} \), n ≠ 0

n=\(\frac{2}{m} \), m ≠ 0

15. j= -2

Hope this helps! Brainliest would be much appreciated! Have a great day! :)

Answer:

here is some

Step-by-step explanation:

1. t=1

2.m=2

3.n=2

4.a=2

STEP 1 : Equation at the end of step 1

(4 +  3 • (x - 7)) -  (3 - x)  = 0

STEP 2 : Pulling out like terms 3.1  

 Pull out like factors : 4x - 20  =   4 • (x - 5) Equation at the end of step 3 : 4 • (x - 5)  = 0

STEP 3 : Equations which are never true 4.1

  Solve :    4   =  0 This equation has no solution. A a non-zero constant never equals zero. Solving a Single Variable Equation: 4.2    

 Solve  :    x-5 = 0

Add  5  to both sides of the equation : x = 5

Answer:   x=5

Answer:

true

Step-by-step explanation:

A correlation is symmetrical;x is as correlated with y as y is with x. The Pearson product-moment correlation can be understood within a regression context,however.

Answer:

a

Step-by-step explanation:

Given

- 6x - x + 10 = 15 - 7x - 5 , that is

- 7x + 10 = - 7x + 10

Since both sides of the equation are equal then all real numbers will make the equation true.

Answer:

B

Step-by-step explanation:

Formula

SA = 2*L*W + 2*L*H + 2*H*W

Givens

L = 14

W = 7

H = 7

Solution

SA = 2*14*7 + 2*14*7 + 2*7*7

SA = 196 + 196 + 98

SA = 490

Answer:

7.a) 5

7.b) 1/2

8. 1

Step-by-step explanation:

7.

a)

Read the points on the graph (0, 0) and (1, 5).

slope = (5 - 0)/(1 - 0) = 5/1 = 5

b)

read the points on the graph (0, 0) and (4, 2).

slope = (2 - 0)/(4 - 0) = 2/4 = 1/2

8.

Points (1, 4) and (5, 8)

slope = (8 - 4)/(5 - 1) = 4/4 = 1

Answer:

hiii my pic lol (✿^‿^)(✿^‿^)(✿^‿^)(✿^‿^)

Answer:

D. 3x + 3 + 6 = 33

Step-by-step explanation:

3(x +1) + 6 = 3

multiply 3 by everything in the parenthesis

3(x) + 3(1) + 6 = 33

3x + 3 + 6 = 33

I hope this helps!

Answer:

x = 3

Step-by-step explanation:

x+5=8

x+5-5=8-5

X=3

Answer:

x = 3

Step-by-step explanation:

basically 2 ways

1st: Transposing

1) x + 5 = 8

2) transpose or transfer +5 to the other side

NOTE: transposing numbers and variables switches the signs (positive -> negative and vice versa)

3) x = 8 - 5

x = 3

2nd: Property of Equality (whatever u do one one side, you do the same to the other)

1) x + 5 = 8

2) x + 5 - 5 = 8 - 5

x = 3

the main focus is to isolate x, or to make it be alone in one side of the equation

Answer:

A = 1160

B = 1160 is already in standard form.

C = 1200

Answer:

The Answer is D

Step-by-step explanation: