(b) region r is the basRegion R is the base of a soli., each cross section perpendicular to the x axis is a semi circle. Write, but do not evaluate, an integral expression that would compute the volume of the solid
of a

Answer:

1378 -3839=10

Step-by-step explanation:

The new protocols, but the fact is a great place for a long time, and it was very nice to be able to get the best the first place in the same manner as the most important part in a row and the rest of us to do with it, but the fact is that it was the only one who thinks and the

Therefore, The explicit formula for the sequence is ak = (1/2)(1)^k + (1/2)(3)^k.

To find an explicit formula for the sequence, we first need to solve the recurrence relation. We can do this by finding the roots of the characteristic equation r^2 - 4r + 3 = 0, which are r = 1 and r = 3. Therefore, the general solution to the recurrence relation is ak = A(1)^k + B(3)^k, where A and B are constants determined by the initial conditions. Plugging in a0 = 1 and a1 = 2, we get the system of equations A + B = 1 and A + 3B = 2. Solving for A and B, we get A = 1/2 and B = 1/2. Therefore, the explicit formula for the sequence is ak = (1/2)(1)^k + (1/2)(3)^k.

Therefore, The explicit formula for the sequence is ak = (1/2)(1)^k + (1/2)(3)^k.

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The system of equations that matches the given graph is:

A. 3x - 6y = 12

9x - 18y = 36

To determine which system of equations matches a given graph, we need to analyze the slope and intercepts of the lines in the graph.

Looking at the options provided:

A. 3x - 6y = 12

9x - 18y = 36

B. 3x + 6y = 12

9x + 18y = 36

Let's analyze the equations in each option:

For option A:

The first equation, 3x - 6y = 12, can be rearranged to slope-intercept form: y = (1/2)x - 2.

The second equation, 9x - 18y = 36, can be simplified to 3x - 6y = 12, which is the same as the first equation.

In option A, both equations represent the same line, as they are equivalent. Therefore, option A does not match the given graph.

For option B:

The first equation, 3x + 6y = 12, can be rearranged to slope-intercept form: y = (-1/2)x + 2.

The second equation, 9x + 18y = 36, can be simplified to 3x + 6y = 12, which is the same as the first equation.

In option B, both equations also represent the same line, as they are equivalent. Therefore, option B does not match the given graph.

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22, 24, 26

Step-by-step explanation:

2n - 2 + 2n + 2n + 2 = 72

6n = 72

n = 72/6

n = 12

∴ so three consecutive even integers whose sum is 72 :

2n - 2

= 2(12) - 2

= 24 - 2

= 22

2n

= 2(12)

= 24

2n + 2

= 2(12) + 2

= 24 + 2

= 26

verification

22 + 24 + 26

= 46 + 26

= 72 ✓✓

The numbers in order from least to greatest are -20, -9, -5, -2, 2.2, 2.5, 2.7

The absolute value of 34 is |34|

The winner of the tournament is Whitney who scored -16.

February 2nd was warmer with a high temperature of 48 °F.

Chicken salad > Hamburger

A system of writing numbers is known as a number system. It is the mathematical notation for consistently employing digits or other symbols to represent the numbers in a particular set.

It represents the arithmetic and algebraic structure of the numbers and gives each number a distinct representation.

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If a hospital medical unit has 50 beds and the unit provided 1,420 days of service, the average daily census for the medical unit in May is 28.4.

To find the average daily census for a medical unit in May, we divide the total number of days of service provided by the number of beds in the unit. Here's how we do it:

According to the question, Total number of beds = 50 and Total number of days of service = 1,420

Average daily census = Total number of days of service / Total number of beds

Average daily census = 1,420/50

Average daily census = 28.4

Therefore, the average daily census for the medical unit in May is 28.4.

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Answer:

10.4476119402

Step-by-step explanation:

If you want a reasonable answer it would be 10.44 or 10.4!

Using the product rule of exponents we will get:

2⁷*2⁻⁵= 2² = (1/2)⁻²

That is the correct option.

Remember the rule for product of powers:

xᵃ*xᵇ = x⁽ᵃ⁺ᵇ⁾

So here we can use that rule to rewrite our expression as:

2⁷*2⁻⁵ = 2⁽⁷⁻⁵⁾ = 2²

The options are written as (1/2) instead of 2 with the base, so can rewrite this as:

(1/2)⁻²

That is the correct option.

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The derivative of f(x) is f'(x) = 1/(2√x) - 6(x + 6)^5.To differentiate the function f(x) = √x - (x + 6)^6, we can apply the chain rule and the power rule.

First, let's differentiate each term separately: d/dx (√x) = (1/2) * x^(-1/2); d/dx (-(x + 6)^6) = -6(x + 6)^5. Now, applying the chain rule, we have: d/dx (√x - (x + 6)^6) = (1/2) * x^(-1/2) - 6(x + 6)^5. Therefore, the derivative of f(x) is given by: f'(x) = (1/2) * x^(-1/2) - 6(x + 6)^5.

Simplifying further, we have: f'(x) = 1/(2√x) - 6(x + 6)^5. So, the derivative of f(x) is f'(x) = 1/(2√x) - 6(x + 6)^5.

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The values of the first term, the common difference and the recursive rule are of the sequences are;

a) first term = 1

Common difference = -5

Recursive rule = aₙ = a₍ₙ ₋ ₁₎ - 5

b) First term = 11

Common difference = 12

Recursive rule is; aₙ = a₍ₙ ₋ ₁₎ + 12

A sequence of numbers is an ordered set of number that follow a specified pattern.

a) The first term is 1

The common difference is; -4 - 1 = -9 - (-4) = -14 - (-9) = -5

The recursive rule is therefore; aₙ = a₍ₙ ₋ ₁₎ - 5

The first term, a₁ = 1

The common difference, d = -5

b) The first term is the term value that comes first in the sequence

The sequence in the question indicates that the first term is 11

The common difference is the difference between a term and the term that comes before it, therefore;

The common difference is; 32 - 11 = 35 - 23 = 47 - 35 = 12

The recursive rule is the first a term is the sum of the previous term and the common difference, therefore;

The recursive rule is; aₙ = a₍ₙ ₋ ₁₎ + 12

The above sequences are arithmetic progressions

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Answer:

Step-by-step explanation:

Combine like terms. The associative and commutative properties of addition apply, as does the distributive property.

__

1. (2x+5)+(3x-2) = (2x +3x) +(5 -2) = 5x +3

__

2. (3x-2)-(2x+5) = 3x -2 -2x -5 = (3x -2x) +(-2 -5) = x -7

__

3. (2x+5)-(3x-2) = 2x +5 -3x +2 = (2x -3x) +(5 +2) = -x +7

_____

Additional comment

Note that swapping the order of operands in a subtraction problem (problems 2 and 3) will cause the sign of the result to reverse.

Answer:

1. = 5x+3

Step-by-step explanation:

The system of equations is consistent and dependent.

The system of equations is given as:

Start by plotting the graph of both equations (see attachment)

From the attached graph, we can see that both equations are represented on a single line.

This means that, the system of equations is consistent and dependent.

This is so because, the system of equations have infinite many solutions.

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Answer:

The probability that Harry will be chosen as either as Secretary or as treasurer but not as president out of those 10 members will be \(\frac{1}{5}\).

Step-by-step explanation:

We have 10 members out of which one is Harry, we need to choose one of the 10 members as President, one to be as secretary out of the remaining 9, one  as the treasurer of the remaining 8 members.

We want harry to be as either as secretary or as treasurer. so we will consider both the cases

Probability is given by = No of favorable outcomes/ Total no of outcomes

(1) Harry as secretary : If harry is to be chosen as secretary then he can't be a president or he cant be a Treasurer

  As president = \(\frac{1}{10}\)

  Not as president = \(1 - \frac{1}{10}\) = \(\frac{9}{10}\)

Now he is selected for the secretary so he can't be selected as treasurer.

Not as treasurer = 1

Probability for chosen as secretary = \(\frac{9}{10}*\frac{1}{9}*1\)  = \(\frac{1}{10}\)  

(2) Harry as treasurer : If harry is to be chosen as the treasurer so he can't be chosen as a President or as a Secretary.

Probability for not chosen as president = \(\frac{9}{10}\)

Probability for not chosen as secretary =  \(1-\frac{1}{9} = \frac{8}{9}\)

Probability to be chosen as treasurer = \(\frac{1}{8}\)

Probability to be chosen as Treasurer = \(\frac{9}{10}*\frac{8}{9}*\frac{1}{8}\) = \(\frac{1}{10}\)

Total probability for Harry to be chosen as either secretary or as treasurer will be = P(Secretary) +P(Treasurer)

           = \(\frac{1}{10} +\frac{1}{10} = \frac{1}{5}\)

Therefore the probability that Harry will be chosen as either as Secretary or as treasurer but not as president out of those 10 members will be \(\frac{1}{5}\).

The Critical point and Point of Inflection for the function f(x) = a/(x² + b²) are (0, a/b²) and (b/√3, 3a/4b²) respectively.

The given function is,

f(x) = a/(x² + b²) = a(x² + b²)⁻¹

Differentiating the function with respect to 'x' we get,

f'(x) = -a(x² + b²)⁻²(2x) = -2ax(x² + b²)⁻²

f''(x) = 2a[-2x(x² + b²)⁻³(2x) + (x² + b²)⁻²] = 2a(x² + b²)⁻²[-4x² + (x² + b²)] = 2a(x² + b²)⁻²[ -3x² + b²]

Now, for critical point,

f'(x) = 0 gives

-2ax(x² + b²)⁻² = 0

x = 0

So, at x = 0, f(0) = a/b²

Hence, (0, a/b²) is the critical point.

For point of Inflection,

f''(x) = 0

2a(x² + b²)⁻²[ -3x² + b²] = 0

3x² = b²

x² = b²/3

x = b/√3

So at x = b/√3, f(b/√3) = 3a/4b²

Hence the point of inflection is (b/√3, 3a/4b²).

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Answer:

the third (bottom left) option

Step-by-step explanation:

for every valid value of x there must be exactly one value of y.

the first option is valid only for positive x, but then for every valid x there are always 2 possible y values (a positive and a negative one).

the second option is defined for only one value of x (3), but this x has infinitely many y values.

the fourth option is a circle defined for -r <= x <= r (r being the radius). in this defined interval almost every x has 2 assigned y values (only x = -r and x = r have one y value).

The graph on the right depicts the linear function y=2x.

Linear function graph is a straight line that depicts linear function y = f(x) = mx + k. It tells the dependent variable y changes by a constant amount as the independent variable x also changes by a constant amount. Whilst variable k is the y-intercept.

The slope of the graph, m, is determined by:

m = (y₂-y₁) / (x₂-x₁)

We are given two graphs. The left graph depicts the line y=x. We want to know what the right graph depicts.

Firstly, we pick two random points on the left graph to find the slope of the graph. Let's say we pick (1,2) and (5,10).

m = (y₂-y₁) / (x₂-x₁)

   = (10-2) / (5-1)

   = 8 / 4

   = 2

Then we find the y-intercept (k), the point where the graph intersects the y-axis. Its value is 0.

Now we put the value of m and k into the linear function:

y = f(x) = mx + k

           = 2x + 0

           = 2x

Thus, the graph on the right shows the line y=2x

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Answer:

Step-by-step explanation:

Let's assume this is a straight line, so we can use the basic form of a straight line equation: y=mx+b, where m is the slope and b is the y-intercept (the value of y when x is zero).

The slope is the rate of change of the line, and can be calculated by dividing the change in y by the change in x between any two points. Here: (0,4) and (1,2)

The change in y is known as the "Rise." Going from (0,4) to (1,2), we have a change of -2:

(2 - 4) = -2 This is the Rise (Final minus the initial values)

X changes by 1 (1-0) = 1 (Final minus the initial values)

Rise/Run = -2/1 or -2

The slope, m, is -2. Values of y decrease as x increases.

The equation becomes y = -2x+b

The value of b must be such it forces the line to go between the two points. We can calculate b by i=using one of the two points in out unfinished equation and solve for b. I'll pick (1,2).

y = -2x+b

2 = -2*(1) + b

b = 4

The equation becomes y=-2x+4

Therefore, the probability of picking a sweet cherry at random from the bag is 5/7.

It is based on the possibility that something might happen. One important aspect of probability theory is the justification for probability. For instance, the theoretical chance of getting a head while tossing a coin is 1 in 2.

The probability of picking a sweet cherry at random can be calculated by dividing the number of sweet cherries by the total number of cherries in the bag:

Probability of picking a sweet cherry = Number of sweet cherries / Total number of cherries

Probability of picking a sweet cherry = 10 / (10 + 4)

Probability of picking a sweet cherry = 10/14

Simplifying the fraction by dividing both numerator and denominator by their greatest common factor (which is 2), we get:

Probability of picking a sweet cherry = 5/7

Therefore, the probability of picking a sweet cherry at random from the bag is 5/7.

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Answer: (1,2)

Step-by-step explanation:

1)

x+y=3

y=-x+3

x | 0 | 3 |

y | 3 | 0 |

2)

3x+y=5

y=-3x+5

x | 0 | 2 |

y | 5 | -1 |

The roots of the quadratic function are:

\(x = -1.5 \pm 1.225i\)

The quadratic equation we want to solve is:

4x^2 + 12x + 15 = 0

To solve this we can use the quadratic formula, we will get:

\(x = \frac{-12 \pm \sqrt{12^2 - 4*4*15} }{2*4} \\\\x = \frac{-12 \pm \sqrt{-96} }{8} \\\\x = \frac{-12 \pm 9.8i}{8}\\\\x = -1.5 \pm 1.225i\)

These are the two complex roots of the quadratic function.

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The answer is 2.6825  cm, which is not one of the given options. Therefore, the correct answer is E. none of these.

The bulk modulus, B is defined as:

B = (P / ΔV / V), where P is the pressure applied, ΔV is the change in volume, and V is the original volume.

For a cube, the change in volume, ΔV is related to the change in length, ΔL by:

\(\sf \Delta V = \Delta L^3\).

Given that the cube has 2.0 cm sides, the original volume, V is:

\(\sf V = (2.0 \ cm)^3 = 8.0 \ cm^3\).

The pressure applied is \(\sf P = 2.0 \times 10^5\) Pa and the bulk modulus is \(\sf B = 4.7 \times 10^5 \ N/m^2\).

We can rearrange the bulk modulus formula to solve for ΔL as:

\(\sf \Delta L = \huge \text(\dfrac{P}{B} \huge \text) \times \dfrac{V}{3}\).

Substituting the values, we get:

\(\sf \Delta L = (2.0 \times 10^5 \ \dfrac{Pa}{4.7} \times 10^5\ N/m^2) \times \dfrac{8.0 \ cm^3}{3} = 0.6825 \ cm\)

Therefore, the final length of any side of the cube is:

\(\sf L = 2.0 \ cm + \Delta L = 2.0 \ cm + 0.6825 \ cm = 2.6825 \ cm\)

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Complete Question:

A cube with 2.0-cm sides is made of material with a bulk modulus of4.7 × 10^5 N/m2. When it is subjected to a pressure of 2.0 × 10^5 Pa the length of its any of its sides is:

A. 0.85 cm

B. 1.15 cm

C. 1.66 cm

D. 2.0 cm

E. none of these

To evaluate \(8^{\frac{2}{3} }\) first find the square of 8 and then take the cube root.

The way of representing huge numbers in terms of powers is known as an exponent. Exponent, then, is the number of times a number has been multiplied by itself.

Depending on the powers they possess, many rules of exponents are given.

Law of Multiplication: Exponents should be added while keeping the base constant when multiplying like bases.

Exponents should be multiplied while bases are kept constant when bases are raised by a power of two or more.

Division Rule: When dividing like bases, maintain the base constant and deduct the exponent of the denominator from the exponent of the numerator.

The given value can be written as:

\(8^{\frac{2}{3} } = \sqrt[3]{8^{2} }\)

Hence, to evaluate \(8^{\frac{2}{3} }\) first find the square of 8 and then take the cube root.

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Answer:

they are parallel lines with a crossing line creating a 90 degree angle

The line A and line B are parallel to each other and line C is perpendicular to both line A nd B.

What is converse of consecutive interior angle theorem ?

As a result of the converse of consecutive interior angle theorem, two parallel lines are formed whenever a transversal intersects two lines so that two consecutive interior angles are supplementary.

Any pair of angles that lie on opposite sides of two lines cut by a transversal on the same side is known as corresponding angle.

Here, the angle ∠d and angle ∠h are corresponding angles and there measurement is 90 degrees which implies that the line A and line B parallel to each other and line C is perpendicular to both line A nd B.

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Answer:

Step-by-step explanation:

The equation x^2 + kx + 5 = 0 has real roots if and only if the discriminant b^2 - 4ac is greater or equal to zero.

In this case, the discriminant is k^2 - 415 = k^2 - 20.

So we know that k^2 - 20 >= 0

therefore k >= sqrt(20) or k <= -sqrt(20)

Two positive values of k are:

k = sqrt(20)

k = sqrt(20) + n, where n is an integer greater than 0

Please note that this is an algebraic solution and doesn't account for any other possibilities that the problem or context may have.

The true statements from the options provided are:

A. The product Ax is defined as a linear combination of columns of A with the corresponding entries of x as weights.

D. The product Ax is a vector in \(R^n\).

E. Ax is a vector whose ith entry is the sum of the products of the corresponding entries from row i of A and the vector x.

A linear combination in mathematics is an expression created from a group of terms by multiplying each component by a constant and combining the results (for example, an expression of the form axe + by, where a and b are constants, would be a linear combination of x and y).

The true statements from the options provided are:

A. The product Ax is defined as a linear combination of columns of A with the corresponding entries of x as weights.

D. The product Ax is a vector in \(R^n\).

E. Ax is a vector whose ith entry is the sum of the products of the corresponding entries from row i of A and the vector x.

These statements accurately describe properties and definitions related to matrix-vector multiplication. The product Ax is obtained by taking a linear combination of the columns of A, where the entries of x act as weights. The resulting product Ax is a vector in \(R^n\), and its entries are calculated by summing the products of the corresponding entries from row i of A and the vector x.

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Answer:

(-8,2)

Step-by-step explanation:

This is because when you reflect a point across the x-axis, the x-coordinate fo the point remains the same and the y-coordinate's sign gets switched.

(x,y) --> (x,-y)

(-8,-2) --> (-8,2)

Answer:

x=-2

Step-by-step explanation:

14+6x=2

Then u move 14 to the other side since it doesn't have a a variable and 2 doesnt also there both just numbers so 14 moved to the otehr side will be -14 so 6x=2-14

6x=-12

x=-12/6=-2

Answer:

= - 2

=

−

2

Step-by-step explanation:

14+6x=2

Then u move 14 to the other side since it doesn't have a a variable and 2 doesnt also there both just numbers so 14 moved to the otehr side will be -14 so 6x=2-14

6x=-12

x=-12/6=-2

Answer:

Step-by-step explanation:544

Answer:

total weight of wheat and rice is 8 kg

Step-by-step explanation:

rice = \(3\frac{3}{2}\)

=3*2+3/2

=9/2

wheat = \(2\frac{1}{2}\)

=2*2+1/2

=5/2

total weight of wheat and rice = \(\frac{7}{2} + \frac{9}{2}\)

since their denominator are same u can add numerators.

=7 +9/2

=16/2

=8

Answer:

$27

Step-by-step explanation:

25 * 0.08 = 2

25 + 2 = 27