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One leg of an isosceles right triangle measures 11 inches. What is the approximate length of the hypotenuse?

To find the value of f'(0), we can use the fact that the integral of f(x)/x²(x+1)³ is a rational function. By examining the properties of the integral, we can determine the value of the derivative at x = 0.

Given that ∫f(x)/x²(x+1)³ dx is a rational function, it implies that the integrand f(x)/x²(x+1)³ is also a rational function. This means that f(x) must be a polynomial function.

Since f(x) is a quadratic function, it can be expressed as f(x) = ax² + bx + c, where a, b, and c are constants. Using the condition f(0) = 1, we have:f(0) = a(0)² + b(0) + c = c = 1. Therefore, the quadratic function f(x) can be written as f(x) = ax² + bx + 1. To find the value of f'(0), we differentiate f(x) with respect to x:

f'(x) = 2ax + b

Now, substituting x = 0 into f'(x), we get:

f'(0) = 2a(0) + b = b

Therefore, the value of f'(0) is equal to the constant term b in the quadratic function f(x) = ax² + bx + 1.

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Answer:

75.40 km³

Step-by-step explanation:

Volume of cone = (1/3) X vertical height X π r ²

= (1/3) X 8 x π (3)²

= (1/3) X 8 X 9π

= (8/3) X 9π

= [(8 X 9) / 3)] π

= (72/3)π

= 24π

= 75.40 km³ to nearest hundredth

The general solution to the differential equation dy/dx = x - 1/3y^2 for y>0 is y(x) = √(3(x^2/2 - x + C)), where C is a constant of integration.

To solve the differential equation, we can separate variables and integrate both sides with respect to y and x:

∫ 1/(y^2 - 3x) dy = ∫ 1 dx

Using partial fraction decomposition, we can rewrite the left-hand side as:

∫ (1/√3) (1/(y + √3x) - 1/(y - √3x)) dy

Integrating each term with respect to y, we get:

(1/√3) ln|y + √3x| - (1/√3) ln|y - √3x| = x + C

Simplifying, we get:

ln|y + √3x| - ln|y - √3x| = √3x + C

ln((y + √3x)/(y - √3x)) = √3x + C

Taking the exponential of both sides and simplifying, we get:

y(x) = √(3(x^2/2 - x + C)), where C is a constant of integration. Therefore, the answer is √(3(x^2/2 - x + C)) for y(x).

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The measures of angles ∠1, ∠3, and ∠4 is 146°, 146°, and 34°.

So, ∠2 = 34°:

Now calculate other angles as follows:

(1) ∠1:

We can easily tell that ∠1 and ∠2 together make a straight angle which makes 180°. Then,

(2) ∠3:

∠1 and ∠3 are a pair of vertically opposite angles and thus are equal.

(3) ∠4:

∠2 and ∠4 are a pair of vertically opposite angles and thus are equal.

Therefore, the measure of angles ∠1, ∠3, and ∠4 is 146°, 146°, and 34°.

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The number of ways to  match 5 of 6 numbers is 6 ways

The number of ways to  match 4 of 6 numbers is 15 ways

The number of ways to  match 3 of 6 numbers is 20 ways

To calculate number of ways to match 5 of 6 numbers we have to use to formula:

\(nCr =\frac{n!}{(n - r)! . r !}\)

\(6C5=\frac{6!}{(6-5)! . 5!}\)

\(6C5=\frac{6!}{(1)! . 5!}\)

\(6C5=\frac{6.5.4.3.2.1}{1.5.4.3.2.1}\)

\(6C5=\frac{6}{1}\)

\(6C5= 6 \ ways\)

∴ 6 ways are to match 5 of 6 numbers

To calculate number of ways to match 4 of 6 numbers we have to use to formula:

\(nCr =\frac{n!}{(n - r)! . r !}\)

\(6C4=\frac{6!}{(6-4)! . 4!}\)

\(6C4=\frac{6!}{(2)! . 4!}\)

\(6C4=\frac{6.5.4.3.2.1}{2.1.4.3.2.1}\)

\(6C4=\frac{30}{2}\)

\(6C4= 15 \ ways\)

∴ 15 ways are to match 4 of 6 numbers

To calculate number of ways to match 4 of 6 numbers we have to use to formula:

\(nCr =\frac{n!}{(n - r)! . r !}\)

\(6C3=\frac{6!}{(6-3)! . 3!}\)

\(6C3=\frac{6!}{(3)! . 3!}\)

\(6C3=\frac{6.5.4.3.2.1}{3.2.1.3.2.1}\)

\(6C3=\frac{120}{6}\)

\(6C3= 20 \ ways\)

∴ 20 ways are to match 3 of 6 numbers

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Step-by-step explanation:

That means the 96 is  75% of your grade

   96 (.75) + 75 (.25) = 90.75  final grade

According to the information provided, k and m are crossing lines with an angle of 86°. We know this because k and m are straight lines.

The angles add up to 180 degrees.

Then we receive,

\(a + 86 =180\)

Or, a = 180 -86

Or, a = 94°.

As a result, an is 94°.

The angle an is 94 degrees.

Supplementary angle are formed when two angles add to 180 degrees. When additional angles are added together, they form a straight angle, or 180 degrees. In these other words, if indeed the sum of angles 1 and 2 equals 180 degrees, angles 1 and 2 are supplementary. Angles 1 and 2 are referred to as "supplements" to one another in this context.

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Answer:

ggycv

Step-by-step explanation:

The range of values that we are permitted to enter into our function is known as the domain of a function. The x values for a function like f make up this set (x). A function's range is the collection of values it can take as input.

The collection of all potential inputs for a function is its domain. For instance, the domain of f(x)=x2 and g(x)=1/x are all real integers with the exception of x=0.

Think about the function y = f. (x). The range of the function is the range of all the y values, from least to maximum. Substitute all possible values of x into the provided expression of y to see whether it is positive, negative, or equal to other values.

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Answer:

22

Step-by-step explanation:

is 22 because 3 times 22 ut maie us 68

Answer:

Let Dad = Y, Son = X

Mathematically, from your statement:

Y = 3X, and (Y+10) + (X+10) = 68

Solving for X in 2nd equation, X = 48-Y

Insert this into first equation and solve for Y:

Y = 3(48-Y)

Y= 144 - 3Y

4Y = 144

Y = 36

Now, solve for X using either equation. I rearranged the 1st equation for X:

X = Y/3

X = 36/3 = 12

The boy is 12 and the dad is 36

Step-by-step explanation:

Hope this helps u

Crown me as brainliest:)

Answer:

This should be correct...

Sorry if I'm wrong :( I'm a little out of practice

hope this helps :)

...........

Answer:

The volume of this composite figure is 312 cubic inches.

Step-by-step explanation:

Volume of pyramid:

\( \frac{1}{3} ( {6}^{2} )(5) = \frac{1}{3} (36)(5) = \frac{1}{3} (180) = 60\)

Volume of rectangular prism:

\(12(3)(7) = 252\)

Volume of composite figure:

\(60 + 252 = 312\)

Answer:

A. \(32/.0333333 = 1\)

   20/ .066666]

   8/.1

   -4/.3

    b. 125

The answer is -\(\frac{(a + 4) ( a +5) }{(a +2)( a - 5)}\)

Simplify is making something simple. In mathematics, simplification means reducing the expression/ fraction/problem in a simpler form by using different operations.  

In the process of simplification, some basic rules are needed to be used. The principle of BODMAS (B= Bracket, O = Of, D = Division, M = Multiplication, A = Addition, S = Subtraction)must be followed for solving the questions.

The equation is :

\(\frac{a^{2} - 16 }{ a^{2} - 25 }\)   ÷   \(\frac{a^{2} - 2a - 8}{a^{2} + 10a + 25}\)

=\(\frac{a^{2} - 4^{2} }{a^{2} - 5^{2} }\)  ÷   \(\frac{a^{2} - 2a - 8}{a^{2} + 10a + 25}\)

= \(\frac{ (a +4 ) ( a - 4 )}{ (a + 5) ( a - 5 )}\)    ÷   \(\frac{a^{2} - 4a + 2a - 8}{a^{2} + 5a + 5a + 25}\) ( by applying middle term factor method)

(using \(a^{2} - b^{2}\) formula )

=  \(\frac{ (a+4) ( a-4 )}{(a +5 ) (a - 5)}\)     ÷      \(\frac{a(a -4) + 2 (a - 4)}{a (a + 5) + a (a + 5)}\) ( by applying middle term factor method)

=\(\frac{( a + 4) ( a - 4)}{( a + 5) ( a - 5)}\)     ÷  \(\frac{(a + 2) ( a -4)}{( a +5) (a+5)}\)

= \(\frac{( a +4)(a-4)}{(a + 5)(a - 5)\\}\)  *   \(\frac{(a + 5) ( a + 5)}{(a + 2) ( a - 4)}\)

=\(\frac{( a + 4) ( a + 5)}{(a + 2) ( a - 5)}\)

so, the answer is - \(\frac{( a + 4 ) ( a +5) }{( a + 2) ( a - 5)}\)

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Answer:

x = 12

Step-by-step explanation:

In ΔABC ≈ ΔQRS , the squiggly line indicates that the triangles are similar meaning that the ratios of the corresponding side lengths are the same.

This means that  \(\frac{AB}{QR} =\frac{BC}{RS} =\frac{CA}{SQ}\)

Here, we are given the side lengths of AB, BC, RQ and we are asked to find the length of x or RS.

We can do so by setting a proportion, and then solving for x.

We've already found out that \(\frac{AB}{QR} =\frac{BC}{RS}\)

So we can plug in the given values and solve for x

Given :

\(\frac{AB}{QR} =\frac{BC}{RS}\)

==> plug in given values

\(\frac{6}{9} =\frac{8}{x}\)

==> cross multiply

6x = 72

==> divide both sides by 6

x = 12

We can check our answer by checking to see if the corresponding sides have similar ratios.

6/9 = 2/3 ✓

8/12 = 2/3 ✓

Answer:

Step-by-step explanation:

The loop will run an infinite number of times

Answer:

14430 pounds

Step-by-step explanation:

Given that:

cost of ring: 13000

percentage increase: 11%

So, to find the new cost, we have to find the increase cost, in pounds:

11 / 100 times 13000 = 1430 pounds.

NOW to calculate the new cost, we add the increase cost to the original:

13000 + 1430 = 14430

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The value of 2x - yz with x = 34, y = 0.2, and z = 6 we get 69.2.

Here it is given that

x = 34

y = -0.2

z = 6

We need to calculate 2x - yz

If we first calculate 2x then we get

2x = 2 X 34

= 68

Now, if we calculate -yz next then we see

yz = -0.2 X 6

= -1.2

Hence

- yz = -(-1.2)

= 1.2

Therefore, adding up these two we get

2x - yz

= 68 + 1.2

= 69.2

Hence the value of 2x - yz is 69.2

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Correct Question

Evaluate the expression 2x - yz , where x = 34 , y = -0.2, and z = 6

bottom was cut off a bit its 4=b

Answer:

The best chart to show how your department's expenses compare to the total company's expenses, and hopefully save employee jobs, would be:

Pie Chart

Step-by-step explanation:

Answer:

The answer would be 1/6

The probability that both jurors selected are female is 1/6.

For a criminal trial, 8 active and 4 alternate jurors are selected.

Two of the alternate jurors are male and two are female.

During the trial, two of the active jurors are dismissed.

The judge decides to randomly select two replacement jurors from the 4 available alternates.

Total numbers of selected candidates is;

8 + 4 = 12

The judge decides to randomly select two replacement jurors from the 4 available alternates.

Therefore,

The probability that both jurors selected are female is;

\(= \dfrac{2}{12}\\\\= \dfrac{1}{6}\)

Hence, the probability that both jurors selected are female is 1/6.

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The solutions of the equation  x² + 2x + 10 = - 3x + 4 are  x=-2 and x=-3

The given equation is x² + 2x + 10 = - 3x + 4.

Take all the terms to the left side

x² + 2x + 10+3x-4=0

Combine the like terms

x²+5x+6=0

x²+2x+3x+6=0

Take out the factors

x(x+2)+3(x+2)=0

(x+3)(x+2)=0

x=-2 and x=-3

Hence, x=-2 and x=-3 are the solutions of the equation  x² + 2x + 10 = - 3x + 4.

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The expected value of the "Buy New" option is 724732.60.

Decision Tree:

To solve the given problem, the first step is to create a decision tree. The decision tree for the given problem is shown below:

Expected Value Calculation: The expected value of the "Buy New" option can be calculated using the following formula:

Expected Value = (Prob. of Prosperity * Payoff for Prosperity) + (Prob. of Recession * Payoff for Recession)

Substituting the given values in the above formula, we get:

Expected Value for "Buy New" = (0.7 * 1,035,332) + (0.3 * -150,000)Expected Value for "Buy New" = 724,732.60

Therefore, the expected value of the "Buy New" option is 724,732.60.

Conclusion:

To conclude, the decision tree is an effective tool used in decision making, especially when the consequences of different decisions are unclear. It helps individuals understand the costs and benefits of different choices and decide the best possible action based on their preferences and probabilities.

The expected value of the "Buy New" option is 724,732.60.

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Answer:

The answer would be C. Inference

The function is not one to one function.

What is one to one function?

A function f(x) is sait to be one to one function if it satisfies the following two conditions:

(1) \(f(x_1)=f(x_2)\) implies \(x_1=x_2\).

(2) ∀\(x_1\), ∀\(x_2\), \(x_1\ne x_2\) implies that \(f(x_1) \ne f(x_2)\).

It means that there is only one value for each value of the variable x.

Now, consider the given function.

\(2(x-1)^2+3=f(x)\)

If it is one to one function then it must satisfy the above two conditions.

Lets check the first condition. Substitute 3 for x.

\(2(3-1)^2+3=f(3)\\11=f(3)\)

Again, substitute -1 for x.

\(2(-1-1)^2+3=f(-1)\\11=f(-1)\)

Hence at two different values of x the function have the same value.

In this case, f(-1)=f(3) but \(-1 \ne 3\). Hence, it do not satisfy the first condition.

Hence, the given function is not one to one function.

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Step-by-step explanation:

C≈62.83m

Using the formulas

C=2πr

d=2r

Solving forC

C=πd=π·20≈62.83185m

The ratio of cups of mixed nuts to cups of granola is 2:11.

A ratio is an ordered pair of numbers a and b, written a / b where b does not equal 0

Given:

Rolled oats= 6 cups

Mixed nuts=2 cups

Sesame seeds=1/2 cup

Cranberries= 1 cup

Dried unsweetened coconuts=1

Honey =1/2 cup

As, the ingredients listed

Total cups of granola= Rolled oats + Mixed nuts + Sesame seeds + Cranberries + Dried unsweetened coconuts + Honey

=6 + 2 + 1/2 + 1 + 1 + 1/2

=11 cups

Hence, the ratio of cups of mixed nuts to cups of granola is 2:11.

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The complete question is

Granola 6 cups rolled oats 2 cups mixed nuts 1 2 cup sesame seeds 1 cup dried cranberries. What is the ratio of cups of mixed nuts to the total number of cups of granola? The ratio of cups of mixed nuts to cups of granola is to . 1 cup dried unsweetened coconut 1 2 cup honey

The modulus of |1 + 2| is √5 and the argument of (1 + z) is π/3. Using Maclaurin series for In (1 + z), we have:In (1 + z) = -2(2 - 1)2/2 + (2 - 1)4/3 - (2 - 1)6/4 + ......... ∞.

Given, |1+2| = √1+2rcost ++².Using the formula for the modulus of the complex number, we have:|1 + 2i| = √(1)2 + (2)2= √5Using the formula for the argument of the complex number, we have:

arg(1 + z)

= arctan(_rsint)

= arctan(_2r/r)

= arctan(2)

(where r = 1 and θ

= π/3)

= π/3

Using Maclaurin series for In (1 + z), we have:

In (1 + z) = z - z2/2 + z3/3 - ....... ∞

= -2(2 - 1)2/2 + (2 - 1)4/3 - (2 - 1)6/4 + ......... ∞

On simplifying, we get:In (1 + z) = -2(2 - 1)2/2 + (2 - 1)4/3 - (2 - 1)6/4 + ......... ∞

= -2(2 - 1)2/2 + (2 - 1)4/3 - (2 - 1)6/4 + ......... ∞.

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